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70. As shown in Figure 27, Lele scored 98 in Math, 88 in Chinese, and after adding English, the average score is 95. Lele scored $\qquad$ in English, and draw the diagram for the English score in the figure.
将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
---
70. As shown in Figure 27, Lele scored 98 in Math, 88 in Chinese, and ... | Reference answer: 99 | 99 | Algebra | math-word-problem | olympiads | 943a8974-e5fa-5b1c-8697-8c6c2515c322 | [
true,
true
] | [
"<think>\n好的，我现在需要解决这个问题。题目是说Lele的数学得了98分，语文88分，加上英语成绩后，平均分变成了95分。要求算出英语成绩，并在图27中画出相应的图表。\n\n首先，我得理解题目的意思。Lele有三门科目：数学、语文和英语。已知数学和语文的成绩分别是98和88，加上英语之后，三门课的平均分是95。所以需要找到英语的成绩，然后画图。\n\n那怎么做呢？平均分是三个分数的总和除以3，等于95。所以，先算三个科目的总分，再减去数学和语文的分数，就能得到英语的分数。\n\n首先，平均分95，总分就是95乘以3，等于285。然后数学和语文加起来是98加88，等于186。所以英语的成绩应该是总分285减去186... | [
false,
true
] | null | null | 1 | [
{
"content": "70. As shown in Figure 27, Lele scored 98 in Math, 88 in Chinese, and after adding English, the average score is 95. Lele scored $\\qquad$ in English, and draw the diagram for the English score in the figure.\n\n将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。\n\n---\n\n70. As shown in Figure 27, Lele scored 98... | <think>
嗯，好的，我现在要解决这个问题。让我仔细看看题目说的是什么。题目是说乐乐在数学得了98分，语文88分，加上英语成绩之后，平均分是95分。然后要算出英语成绩，并且在图27里画出英语成绩的图表。
首先，我需要确定已知条件和所求的答案。已知数学98，语文88，英语成绩未知，设为x。三科的平均分是95。平均分等于总分除以科目数，这里三科，所以总分应该是95乘以3。那总分应该是95×3=285分。数学和语文加起来是98+88=186分。所以英语成绩应该是总分减去这两科的总分，也就是285-186=99分。那这样算的话，英语应该是99分对吗？
不过让我再检查一下，确保自己没算错。数学98，语文88，加起来是186。平均分95... | 804 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
70. As shown in Figure 27, Lele scored 98 in Math, 88 in Chinese, and after adding English, the average score is 95. Lele scored $\qquad$ in English, and draw the diagram for the English score in the figur... |
5. Let $t$ be a real root of the quadratic equation $a x^{2}+b x+c=0(a \neq 0)$, then the relationship between the discriminant $\Delta=b^{2}-4 a c$ and the quadratic form $M=(2 a t+b)^{2}$ is ( ).
(A) $\Delta>M$
(B) $\Delta=M$.
(C) $\Delta<M$
(D) Cannot be determined
直接输出翻译结果。 | 5. B (Hint: Since $t$ is a root of the equation, we have $a t^{2}+b t+c=0$. Thus, $M=4 a^{2} t^{2}+4 a b t+b^{2}=4 a\left[a t^{2}+b t+c\right]-4 a c$ $+b^{2}=b^{2}-4 a c=\Delta.$) | B | Algebra | MCQ | cn_contest | fde31125-1508-5847-9687-42d3d8026506 | [
true,
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"<think>\n\n</think>\n\n题目：设 \\( t \\) 是二次方程 \\( a x^{2} + b x + c = 0 \\)（\\( a \\neq 0 \\)）的一个实根，则判别式 \\( \\Delta = b^{2} - 4ac \\) 与二次形式 \\( M = (2at + b)^{2} \\) 的关系是（ ）。\n(A) \\( \\Delta > M \\)\n(B) \\( \\Delta = M \\)\n(C) \\( \\Delta < M \\)\n(D) 无法确定\n\n**解答过程：**\n\n1. **已知条件：**\n - \\( t \\) 是方程 \\( a x... | [
false,
true,
true,
true
] | null | null | 3 | [
{
"content": "5. Let $t$ be a real root of the quadratic equation $a x^{2}+b x+c=0(a \\neq 0)$, then the relationship between the discriminant $\\Delta=b^{2}-4 a c$ and the quadratic form $M=(2 a t+b)^{2}$ is ( ).\n(A) $\\Delta>M$\n(B) $\\Delta=M$.\n(C) $\\Delta<M$\n(D) Cannot be determined\n\n直接输出翻译结果。",
"... | <think>
</think>
你将遇到一个问题。请逐步思考，并将最终答案放在\boxed{}中：
5. 设 \( t \) 是二次方程 \( a x^{2} + b x + c = 0 \)（\( a \neq 0 \)）的一个实根，则判别式 \( \Delta = b^{2} - 4 a c \) 与二次形式 \( M = (2 a t + b)^{2} \) 的关系是（ ）。
(A) \( \Delta > M \)
(B) \( \Delta = M \)
(C) \( \Delta < M \)
(D) 无法确定
**解答过程：**
1. **已知条件：**
- \( t \) 是方程 \( a x^{2... | 884 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
5. Let $t$ be a real root of the quadratic equation $a x^{2}+b x+c=0(a \neq 0)$, then the relationship between the discriminant $\Delta=b^{2}-4 a c$ and the quadratic form $M=(2 a t+b)^{2}$ is ( ).
(A) $\D... |
8. If the line $2 x+y-2=0$ is perpendicular to the line $x+m y-1=0$, then the distance from point $P(m, m)$ to the line $x+y+3=0$ is
保留源文本的换行和格式，直接输出翻译结果。 | Given that $2+m=0 \Rightarrow m=-2$, the distance from point $P(m, m)$ to the line $x+y+3=0$ is $d=\frac{|-2-2+3|}{\sqrt{2}}=\frac{\sqrt{2}}{2}$. | \frac{\sqrt{2}}{2} | Algebra | math-word-problem | olympiads | 501248f9-a071-525a-950d-e200e202d3bf | [
true,
true,
true,
true
] | [
"<think>\n\n</think>\n\n我们将被给予一个问题。请逐步推理，并将最终答案放在\\boxed{}中：\n8. 如果直线$2x + y - 2 = 0$与直线$x + my - 1 = 0$垂直，那么点$P(m, m)$到直线$x + y + 3 = 0$的距离是\n\n保留源文本的换行和格式，直接输出翻译结果。\n\n\\boxed{\\sqrt{2}}",
"<think>\n\n</think>\n\n我们将被给予一个问题。请逐步推理，并将最终答案放在 \\boxed{} 中：\n8. 如果直线 \\(2x + y - 2 = 0\\) 与直线 \\(x + my - 1 = 0\\) 垂直，则点... | [
false,
false,
true,
false
] | null | null | 1 | [
{
"content": "8. If the line $2 x+y-2=0$ is perpendicular to the line $x+m y-1=0$, then the distance from point $P(m, m)$ to the line $x+y+3=0$ is\n\n保留源文本的换行和格式，直接输出翻译结果。",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\n我们将被给予一个问题。请逐步推理，并将最终答案放在\\boxed{}中：\n\n8. 如果直线 \\(2x + y - 2 = 0\\) 与直... | <think>
</think>
我们将被给予一个问题。请逐步推理，并将最终答案放在\boxed{}中：
8. 如果直线 \(2x + y - 2 = 0\) 与直线 \(x + my - 1 = 0\) 垂直，那么点 \(P(m, m)\) 到直线 \(x + y + 3 = 0\) 的距离是
保留源文本的换行和格式，直接输出翻译结果。
---
**解答：**
**步骤1：确定两直线垂直的条件**
两条直线垂直的条件是它们的斜率的乘积为-1。
- 直线 \(2x + y - 2 = 0\) 的斜率为 \(k_1 = -2\)。
- 直线 \(x + my - 1 = 0\) 的斜率为 \(k_2 = -\frac... | 898 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
8. If the line $2 x+y-2=0$ is perpendicular to the line $x+m y-1=0$, then the distance from point $P(m, m)$ to the line $x+y+3=0$ is
保留源文本的换行和格式，直接输出翻译结果。<|im_end|>
<|im_start|>assistant
<|im_start|>think... |
9. $x, y \in \mathbf{R}^{+}, 3x+2y=12, xy$ 的最大值为
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
9. $x, y \in \mathbf{R}^{+}, 3x+2y=12, xy$'s maximum value is | 9. 6. $x y=\frac{1}{6}(3 x)(2 y) \leqslant \frac{1}{6} \cdot\left(\frac{3 x+2 y}{2}\right)^{2}=6$. | 6 | Algebra | math-word-problem | olympiads | 8ac3b4f3-2de1-57d3-8a8e-2035d9dec8b3 | [
true,
true
] | [
"<think>\n\n</think>\n\n9. $x, y \\in \\mathbf{R}^{+}, 3x+2y=12$, the maximum value of $xy$ is\n\n**Solution:** \nGiven the constraint \\( 3x + 2y = 12 \\), we aim to maximize \\( xy \\).\n\n1. **Express \\( y \\) in terms of \\( x \\):** \n From the constraint: \n \\[\n 2y = 12 - 3x \\implies y = \\frac{1... | [
true,
true
] | null | null | 2 | [
{
"content": "9. $x, y \\in \\mathbf{R}^{+}, 3x+2y=12, xy$ 的最大值为\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.\n\n9. $x, y \\in \\mathbf{R}^{+}, 3x+2y=12, xy$'s maximum value is",
"role": "user"
},
{
"c... | <think>
</think>
9. $x, y \in \mathbf{R}^{+}, 3x+2y=12$, the maximum value of $xy$ is
**Solution:**
Given the constraint \( 3x + 2y = 12 \), we aim to maximize \( xy \).
1. **Express \( y \) in terms of \( x \):**
From the constraint:
\[
2y = 12 - 3x \implies y = \frac{12 - 3x}{2}
\]
2. **Substit... | 1,045 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
9. $x, y \in \mathbf{R}^{+}, 3x+2y=12, xy$ 的最大值为
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
9. $x, y \in ... |
## Task 2
In the shot put, the first one achieves 19 meters. The second one reaches 2 meters less.
How many meters does the second one reach? | $19-2=17$; The second one reaches 17 meters.
### 10.9 11th Olympiad 1973
### 10.9.1 1st Round 1973, Class 1 | 17 | Algebra | math-word-problem | olympiads | 0346efdc-eee1-5e14-9e9c-1deddc4a6321 | [
true,
true
] | [
"<think>\nOkay, so let's see here. The problem is about the shot put. The first person throws 19 meters, and the second one reaches 2 meters less. I need to find out how far the second one threw. Hmm, okay.\n\nAlright, first, the first athlete's distance is 19 meters. The second one is 2 meters less than that. So I... | [
true,
true
] | null | null | 2 | [
{
"content": "## Task 2\n\nIn the shot put, the first one achieves 19 meters. The second one reaches 2 meters less.\n\nHow many meters does the second one reach?",
"role": "user"
},
{
"content": "<think>\nOkay, so let's see here. The problem is about the shot put. The first person throws 19 meters, ... | <think>
Okay, so there's this problem about shot put. The first person throws 19 meters, and the second one reaches 2 meters less. I need to find out how far the second one threw. Hmm, let's see.
Alright, first, the first athlete's distance is 19 meters. The second one is 2 meters less than that. So, I think I just su... | 1,147 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 2
In the shot put, the first one achieves 19 meters. The second one reaches 2 meters less.
How many meters does the second one reach?<|im_end|>
<|im_start|>assistant
<|im_start|>think
Okay, so t... |
## Task 6
Peter has 12 pennies, Annett gives him enough so that he has 20 pennies.
How much money does Annett give? Write an equation. | Annett gives 8 pennies. $12+8=20$
### 10.26 28th Olympiad 1990
### 10.26.1 1st Round 1990, Class 1 | 8 | Algebra | math-word-problem | olympiads | f4a234c6-8131-5c6e-b834-a0b5a04c7f77 | [
true,
true
] | [
"<think>\nOkay, let's see. So Peter starts with 12 pennies. Then Annett gives him some more, and after that, he has 20 pennies. The question is asking how much money Annett gave him, and we need to write an equation for that.\n\nHmm, let's break it down. Peter initially has 12 pennies. Let's call the amount Annett ... | [
true,
true
] | null | null | 2 | [
{
"content": "## Task 6\n\nPeter has 12 pennies, Annett gives him enough so that he has 20 pennies.\n\nHow much money does Annett give? Write an equation.",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. So Peter starts with 12 pennies. Then Annett gives him some more, and after that, he ... | <think>
Okay, let's see. So Peter starts with 12 pennies. Then Annett gives him some more, and after that, he has 20 pennies. The question is asking how much money Annett gave him, and we need to write an equation for that.
Hmm, let's break it down. Peter initially has 12 pennies. Let's call the amount Annett gives hi... | 1,242 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 6
Peter has 12 pennies, Annett gives him enough so that he has 20 pennies.
How much money does Annett give? Write an equation.<|im_end|>
<|im_start|>assistant
<|im_start|>think
Okay, let's see. ... |
Example 4 If $a, b, c$ are non-negative real numbers and $a+b+c=1$, try to find the maximum value of $S=ab+bc+ca-3abc$.
保留源文本的换行和格式，直接输出翻译结果。 | Let's assume $a \geqslant b \geqslant c$, then $c \leqslant \frac{1}{3}$. Fix $c$,
$$S=a b+b c+c a-3 a b c=a b(1-3 c)+c(a+b)$$
Since the value of $a+b$ is fixed, $1-3 c \geqslant 0$, and $a b$ reaches its maximum value when $a=b$, hence $S$ reaches its maximum value when $a=b$.
Adjust $a, b, c$ to $a=b \geqslant c$, ... | \frac{1}{4} | Algebra | math-word-problem | inequalities | 1ebed677-af3d-54be-a9b8-811fa6498555 | [
true,
true
] | [
"<think>\n\n</think>\n\n我们将面对以下问题：已知 \\(a, b, c\\) 是非负实数且满足 \\(a + b + c = 1\\)，尝试求出 \\(S = ab + bc + ca - 3abc\\) 的最大值。\n\n**分析与解答**\n\n1. **对称性与极值位置** \n 由于表达式 \\(S\\) 对于 \\(a, b, c\\) 是对称的，我们推测其极值可能出现在变量相等或部分变量为0的位置。\n\n2. **情况一：单变量为0（例如 \\(c = 0\\)）** \n 此时问题简化为 \\(a + b = 1\\)，求 \\(S = ab\\) 的最大值。 \n ... | [
true,
true
] | null | null | 2 | [
{
"content": "Example 4 If $a, b, c$ are non-negative real numbers and $a+b+c=1$, try to find the maximum value of $S=ab+bc+ca-3abc$.\n\n保留源文本的换行和格式，直接输出翻译结果。",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\n我们将面对以下问题：已知 \\(a, b, c\\) 是非负实数且满足 \\(a + b + c = 1\\)，尝试求出 \\(S = ab + bc + ca - 3... | <think>
</think>
我们将面对以下问题：已知 \(a, b, c\) 是非负实数且满足 \(a + b + c = 1\)，尝试求出 \(S = ab + bc + ca - 3abc\) 的最大值。
**分析与解答**
1. **对称性与极值位置**
由于表达式 \(S\) 对于 \(a, b, c\) 是对称的，我们推测其极值可能出现在变量相等或部分变量为0的位置。
2. **情况一：单变量为0（例如 \(c = 0\)）**
此时问题简化为 \(a + b = 1\)，求 \(S = ab\) 的最大值。
根据均值不等式，\(ab \leq \left(\frac{a + ... | 1,259 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Example 4 If $a, b, c$ are non-negative real numbers and $a+b+c=1$, try to find the maximum value of $S=ab+bc+ca-3abc$.
保留源文本的换行和格式，直接输出翻译结果。<|im_end|>
<|im_start|>assistant
<|im_start|>think
<|im_start... |
## Task 2
Multiply the numbers 7 and 6. Subtract 5 from the product.
Write the equation and solve.
| $7 \cdot 6-5=37$
### 11.9 10th Olympiad 1972
### 11.9.1 1st Round 1972, Class 2 | 37 | Algebra | math-word-problem | olympiads | 7a2c27c7-3adf-5bed-a067-dd03d8bb91c0 | [
true,
true
] | [
"<think>\nOkay, let's see. The problem says to multiply 7 and 6 and then subtract 5 from the product. Hmm, right. So first, I need to figure out what 7 times 6 is. Let me calculate that. 7 multiplied by 6... well, 7 times 5 is 35, and then adding another 7 makes 42. So the product of 7 and 6 is 42.\n\nNow, the next... | [
true,
true
] | null | null | 2 | [
{
"content": "## Task 2\n\nMultiply the numbers 7 and 6. Subtract 5 from the product.\n\nWrite the equation and solve.\n\n",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. The problem says to multiply 7 and 6 and then subtract 5 from the product. Hmm, right. So first, I need to figure out... | <think>
Okay, let's see. The problem says to multiply 7 and 6 and then subtract 5 from the product. Hmm, right. So first, I need to figure out what 7 times 6 is. Let me calculate that. 7 multiplied by 6... well, 7 times 5 is 35, and then adding another 7 makes 42. So the product of 7 and 6 is 42.
Now, the next step is... | 1,346 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 2
Multiply the numbers 7 and 6. Subtract 5 from the product.
Write the equation and solve.
<|im_end|>
<|im_start|>assistant
<|im_start|>think
Okay, let's see. The problem says to multiply 7 and... |
## Task 1
Calculate the sum of the numbers 6 and 4. Add the number 30 to this sum. | $6+4=10 ; 10+30=40$ | 40 | Algebra | math-word-problem | olympiads | 54925800-ab24-5a90-8ff7-1be47f89a4f5 | [
true,
true
] | [
"<think>\nOkay, let's see here. I need to calculate the sum of 6 and 4 first. So, adding those two numbers together. Let me do that step by step. 6 plus 4... that should be 10, right? Yeah, 6 plus 4 equals 10.\n\nNow, the next part says to add 30 to this sum. The sum we just got was 10. So, adding 30 to 10. Hmm, 10... | [
true,
true
] | null | null | 2 | [
{
"content": "## Task 1\n\nCalculate the sum of the numbers 6 and 4. Add the number 30 to this sum.",
"role": "user"
},
{
"content": "<think>\nOkay, let's see here. I need to calculate the sum of 6 and 4 first. So, adding those two numbers together. Let me do that step by step. 6 plus 4... that shou... | <think>
Okay, let's see. The problem is to calculate the sum of 6 and 4 first, and then add 30 to that sum. Hmm, right. So first step is to add 6 and 4. Let me make sure I understand that correctly.
So, 6 plus 4. Let me count that. 6 plus 4 equals... 6, 7, 8, 9, 10. Yeah, that's 10. Okay, so the sum of 6 and 4 is 10. ... | 1,376 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 1
Calculate the sum of the numbers 6 and 4. Add the number 30 to this sum.<|im_end|>
<|im_start|>assistant
<|im_start|>think
Okay, let's see. The problem is to calculate the sum of 6 and 4 first,... |
## Task 2
In sports, all children are trying very hard. Horst throws the ball 18 meters far. Ines only reaches half of that. Claudia throws the ball 5 meters further than Ines.
a) How many meters does Ines reach?
b) How far does Claudia throw her ball? | $18: 2=9$; Ines reaches $9 \mathrm{~m} .9+5=14$; Claudia throws her ball $14 \mathrm{~m}$ far. | 14\mathrm{~} | Algebra | math-word-problem | olympiads | caa6a4d2-58ab-5bc2-ac0b-385e96d32389 | [
true,
true
] | [
"<think>\nOkay, let's see. I need to solve part a) first. The problem says Horst throws the ball 18 meters far. Ines only reaches half of that. So, Ines's throw is half of Horst's. Horst is 18 meters, so half of that would be 18 divided by 2. Let me calculate that. 18 divided by 2 is 9. So Ines reaches 9 meters. Th... | [
false,
true
] | null | null | 1 | [
{
"content": "## Task 2\n\nIn sports, all children are trying very hard. Horst throws the ball 18 meters far. Ines only reaches half of that. Claudia throws the ball 5 meters further than Ines.\n\na) How many meters does Ines reach?\n\nb) How far does Claudia throw her ball?",
"role": "user"
},
{
"c... | <think>
Okay, let's tackle part a) first. The problem says Horst throws the ball 18 meters far. Ines only reaches half of that. So, I need to find half of 18 meters to determine how far Ines threw the ball.
Half of 18 is calculated by dividing 18 by 2. Let me do that: 18 ÷ 2 = 9. So, Ines reaches 9 meters. That seems ... | 1,403 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 2
In sports, all children are trying very hard. Horst throws the ball 18 meters far. Ines only reaches half of that. Claudia throws the ball 5 meters further than Ines.
a) How many meters does In... |
## Task 4
Add the numbers 1 to 10. | $1+2+3+4+5+6+7+8+9+10=55$. The sum is 55. | 55 | Algebra | math-word-problem | olympiads | e6d0f049-80f4-544e-8df5-5bea731426bb | [
true,
true
] | [
"<think>\nOkay, let's see. I need to add all the numbers from 1 to 10. Hmm, how do I do that? Well, I could just start adding them one by one. Let me try that first.\n\nStarting with 1 plus 2, that's 3. Then add 3, which makes 6. Next, add 4 to get 10. Then 5 added to 10 is 15. Wait, let me check that again. 1+2 is... | [
true,
true
] | null | null | 2 | [
{
"content": "## Task 4\n\nAdd the numbers 1 to 10.",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. I need to add all the numbers from 1 to 10. Hmm, how do I do that? Well, I could just start adding them one by one. Let me try that first.\n\nStarting with 1 plus 2, that's 3. Then add 3, ... | <think>
Okay, let's see. I need to add all the numbers from 1 to 10. Hmm, how do I do that? Well, I could just start adding them one by one. Let me try that.
Starting with 1 plus 2, that's 3. Then add 3, so 3 plus 3 is 6. Next, add 4. 6 plus 4 is 10. Then add 5. 10 plus 5 equals 15. Now, adding 6 to 15 gives me 21. Th... | 1,406 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 4
Add the numbers 1 to 10.<|im_end|>
<|im_start|>assistant
<|im_start|>think
Okay, let's see. I need to add all the numbers from 1 to 10. Hmm, how do I do that? Well, I could just start adding th... |
## Task 6
Multiply 8 by 4, subtract 15 from the product. | $8 \cdot 4=32 ; 32-15=17$
### 11.15.2 2. Round 1978, Class 2 | 17 | Algebra | math-word-problem | olympiads | 6803f90a-4e5d-57c7-83fb-826eed2566aa | [
true,
true
] | [
"<think>\nOkay, let's tackle this problem step by step. The question says to multiply 8 by 4 and then subtract 15 from the product. Alright, first things first, I need to handle the multiplication part.\n\nSo, multiplying 8 by 4. Let me make sure I remember my times tables. 8 times 4... Hmm, 8 added four times: 8 +... | [
true,
true
] | null | [
"stop",
"stop"
] | 2 | [
{
"content": "## Task 6\n\nMultiply 8 by 4, subtract 15 from the product.",
"role": "user"
},
{
"content": "<think>\nOkay, let's tackle this problem step by step. The question says to multiply 8 by 4 and then subtract 15 from the product. Alright, first things first, I need to handle the multiplicat... | <think>
Okay, let's tackle this problem step by step. The question says to multiply 8 by 4 and then subtract 15 from the product. Alright, first things first, I need to handle the multiplication part.
So, multiplying 8 by 4. Let me make sure I remember my times tables. 8 times 4... Hmm, 8 added four times: 8 + 8 is 16... | 1,451 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 6
Multiply 8 by 4, subtract 15 from the product.<|im_end|>
<|im_start|>assistant
<|im_start|>think
Okay, let's tackle this problem step by step. The question says to multiply 8 by 4 and then subt... |
1. (8 points) Calculate: $12+34 \times 15-78$, the result obtained is
保留源文本的换行和格式，直接输出翻译结果如下：
1. (8 points) Calculate: $12+34 \times 15-78$, the result obtained is | 【Solution】Solution: $12+34 \times 15-78$
$$
\begin{array}{l}
=12+510-78 \\
=522-78 \\
=444
\end{array}
$$
Therefore, the answer is: 444. | 444 | Algebra | math-word-problem | olympiads | cbbddc23-2938-5e20-aa9a-ded22f691c96 | [
true,
true
] | [
"<think>\n好的，我现在要解决这个数学题：计算12加34乘以15减78的结果。首先，我得仔细看看题目，确保自己理解正确。题目是12加上34乘以15，然后再减去78，对吧？嗯，对，这里需要按照运算顺序来进行计算，也就是先乘除后加减，对吧？\n\n那我先回想一下运算顺序的规则，也就是常说的PEMDAS或者BODMAS法则。PEMDAS代表括号、指数、乘除、加减，而BODMAS则是括号、顺序、除乘、加减，其实两者都差不多，都是先做乘除后做加减。所以在这道题里，应该先计算34乘以15，然后再处理加和减的部分。\n\n首先，我来算乘法部分：34乘以15。嗯，这个乘法可能需要分步骤来做。比如，我可以把15拆成10加5，这样34乘... | [
true,
true
] | null | null | 2 | [
{
"content": "1. (8 points) Calculate: $12+34 \\times 15-78$, the result obtained is\n\n保留源文本的换行和格式，直接输出翻译结果如下：\n\n1. (8 points) Calculate: $12+34 \\times 15-78$, the result obtained is",
"role": "user"
},
{
"content": "<think>\n好的，我现在要解决这个数学题：计算12加34乘以15减78的结果。首先，我得仔细看看题目，确保自己理解正确。题目是12加上34乘以15，然后再... | <think>
好的，我现在要解决这个数学题：计算12加34乘以15减78的结果。首先，我得仔细看看题目，确保自己理解正确。题目是12加上34乘以15，然后再减去78，对吧？嗯，对，这里需要按照运算顺序来进行计算，也就是先乘除后加减，对吧？
那我先回想一下运算顺序的规则，也就是常说的PEMDAS或者BODMAS法则。PEMDAS代表括号、指数、乘除、加减，而BODMAS则是括号、顺序、除乘、加减，其实两者都差不多，都是先做乘除后做加减。所以在这道题里，应该先计算34乘以15，然后再处理加和减的部分。
首先，我来算乘法部分：34乘以15。嗯，这个乘法可能需要分步骤来做。比如，我可以把15拆成10加5，这样34乘以10就是340，加... | 1,514 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
1. (8 points) Calculate: $12+34 \times 15-78$, the result obtained is
保留源文本的换行和格式，直接输出翻译结果如下：
1. (8 points) Calculate: $12+34 \times 15-78$, the result obtained is<|im_end|>
<|im_start|>assistant
<|im_st... |
## Task 2
Tanja thinks of a number, triples it, and adds 25. Her result is 40. What number did Tanja think of? Set up an equation for this calculation. | $x \cdot 3+25=40$, i.e., the thought number is 5.
### 13.14 25th Olympiad 1987
### 13.14.1 1st Round 1987, Class 4 | 5 | Algebra | math-word-problem | olympiads | d2a85914-2413-5728-a7b6-a97835b4357d | [
true,
true
] | [
"<think>\nOkay, let's see. Tanja thinks of a number, triples it, and adds 25. Her result is 40. I need to find out what number she thought of. Hmm, let me break this down step by step.\n\nFirst, let's denote the unknown number she thought of as a variable. Let's call it x. So, if Tanja triples her number, that woul... | [
true,
false
] | null | null | 1 | [
{
"content": "## Task 2\n\nTanja thinks of a number, triples it, and adds 25. Her result is 40. What number did Tanja think of? Set up an equation for this calculation.",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. Tanja thinks of a number, triples it, and adds 25. Her result is 40. I ... | <think>
Okay, let's see. Tanja thinks of a number, triples it, and adds 25. Her result is 40. I need to find out what number she thought of. Hmm, let me break this down step by step.
First, let's denote the unknown number she thought of as a variable. Let's call it x. So, if Tanja triples her number, that would be 3 t... | 1,549 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 2
Tanja thinks of a number, triples it, and adds 25. Her result is 40. What number did Tanja think of? Set up an equation for this calculation.<|im_end|>
<|im_start|>assistant
<|im_start|>think
O... |
## Task 1
What is the number?
If I subtract a number from 12, I get 7. Calculate! | The number is 5 . | 5 | Algebra | math-word-problem | olympiads | a749b290-a711-5981-ba2f-db263276c4f2 | [
true,
true
] | [
"<think>\nOkay, so I need to find a number such that when I subtract it from 12, the result is 7. Hmm, let me think about how to set this up. The problem says \"If I subtract a number from 12, I get 7.\" Let me write that down as an equation. \n\nWhen they say \"subtract a number from 12,\" that translates to 12 mi... | [
true,
true
] | null | null | 2 | [
{
"content": "## Task 1\n\nWhat is the number?\n\nIf I subtract a number from 12, I get 7. Calculate!",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find a number such that when I subtract it from 12, the result is 7. Hmm, let me think about how to set this up. The problem says \"If I... | <think>
Okay, let's see. The problem says, "If I subtract a number from 12, I get 7. Calculate!" Hmm, so I need to find the number that when subtracted from 12 gives 7. Let me think about how to set this up.
So, subtracting a number from 12... In math terms, that would be 12 minus the number equals 7. Let me write tha... | 1,585 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 1
What is the number?
If I subtract a number from 12, I get 7. Calculate!<|im_end|>
<|im_start|>assistant
<|im_start|>think
Okay, let's see. The problem says, "If I subtract a number from 12, I ... |
## Task 2
Subtract 7 from $x$. The result is 8.
Write the equation! What is the number $x$? | $x-7=8 ; x=15$
### 10.8 10th Olympiad 1972
### 10.8.1 1st Round 1972, Class 1 | 15 | Algebra | math-word-problem | olympiads | d8c8b4e9-7187-57a1-8734-a4713f53b7a0 | [
true,
true
] | [
"<think>\nOkay, let's see. The problem says to subtract 7 from x, and the result is 8. I need to write an equation and find the value of x. Alright, let's break it down step by step.\n\nFirst, understanding the words: \"Subtract 7 from x.\" So, that means taking x and then removing 7 from it. In mathematical terms,... | [
true,
true
] | null | null | 2 | [
{
"content": "## Task 2\n\nSubtract 7 from $x$. The result is 8.\n\nWrite the equation! What is the number $x$?",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. The problem says to subtract 7 from x, and the result is 8. I need to write an equation and find the value of x. Alright, let's ... | <think>
Okay, let's see. The problem says to subtract 7 from x, and the result is 8. I need to write an equation and find the value of x. Alright, let's break it down step by step.
First, understanding the words: "Subtract 7 from x." So, that means taking x and then removing 7 from it. In mathematical terms, subtracti... | 1,593 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
## Task 2
Subtract 7 from $x$. The result is 8.
Write the equation! What is the number $x$?<|im_end|>
<|im_start|>assistant
<|im_start|>think
Okay, let's see. The problem says to subtract 7 from x, and ... |
1. (8 points) The calculation result of the expression $210+6-12-19$ is
保留了源文本的换行和格式，但请注意，最后一句“保留了源文本的换行和格式”是说明性质的，不应包含在翻译结果中。正确的翻译结果如下：
1. (8 points) The calculation result of the expression $210+6-12-19$ is | 1. (8 points) The calculation result of the expression $210+6-12-19$ is $\qquad$ 185 .
【Solution】Solution: $210+6-12$ - 19
$$
\begin{array}{l}
=216-12-19 \\
=204-19 \\
=185
\end{array}
$$
Therefore, the answer is: 185 . | 185 | Algebra | math-word-problem | olympiads | 04184f0c-c3d8-541b-8311-3d0990445acf | [
true,
true
] | [
"<think>\n嗯，好的，我现在得算一下这个表达式的结果：210加6减12再减19。让我慢慢想想，别急着下结论，先仔细一步步来。\n\n首先，我得按照运算的顺序来做，不过这里都是加减法，所以应该从左到右依次计算对吧。先看第一个数，是210，然后加上6，对吧？那210加6等于多少呢？让我算一下，210加6的话，个位是0加6等于6，十位和百位不变，所以应该是216。对，没错，第一步得到的是216。\n\n接下来要减去12。现在的问题就是216减12是多少。嗯，216减去10的话是206，然后再减去2，就是204。所以这一步的结果应该是204。对吗？再确认一下，216减12，分解的话，216-10=206，再减2就是204，没... | [
true,
true
] | null | null | 2 | [
{
"content": "1. (8 points) The calculation result of the expression $210+6-12-19$ is\n\n保留了源文本的换行和格式，但请注意，最后一句“保留了源文本的换行和格式”是说明性质的，不应包含在翻译结果中。正确的翻译结果如下：\n\n1. (8 points) The calculation result of the expression $210+6-12-19$ is",
"role": "user"
},
{
"content": "<think>\n嗯，好的，我现在得算一下这个表达式的结果：210加6减1... | <think>
嗯，好的，我现在得算一下这个表达式的结果：210加6减12再减19。让我慢慢想想，别急着下结论，先仔细一步步来。
首先，我得按照运算的顺序来做，不过这里都是加减法，所以应该从左到右依次计算对吧。先看第一个数，是210，然后加上6，对吧？那210加6等于多少呢？让我算一下，210加6的话，个位是0加6等于6，十位和百位不变，所以应该是216。对，没错，第一步得到的是216。
接下来要减去12。现在的问题就是216减12是多少。嗯，216减去10的话是206，然后再减去2，就是204。所以这一步的结果应该是204。对吗？再确认一下，216减12，分解的话，216-10=206，再减2就是204，没错。
然后下一步是... | 1,628 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
1. (8 points) The calculation result of the expression $210+6-12-19$ is
保留了源文本的换行和格式，但请注意，最后一句“保留了源文本的换行和格式”是说明性质的，不应包含在翻译结果中。正确的翻译结果如下：
1. (8 points) The calculation result of the expression $210+6-12-1... |
2. (5 points) Given $a=0.5, b=\frac{1}{3}$, then $a-b$ is $\frac{1}{78}$ of $\qquad$ times
保留源文本的换行和格式，翻译结果如下：
2. (5 points) Given $a=0.5, b=\frac{1}{3}$, then $a-b$ is $\frac{1}{78}$ of $\qquad$ times | 【Solution】Solve: $(a-b) \div \frac{1}{78}$
$$
\begin{array}{l}
=\left(0.5-\frac{1}{3}\right) \div \frac{1}{78} \\
=\left(\frac{1}{2}-\frac{1}{3}\right) \div \frac{1}{78} \\
=\frac{1}{6} \div \frac{1}{78} \\
=13
\end{array}
$$
Therefore, the answer is: 13. | 13 | Algebra | math-word-problem | olympiads | f10e154e-3936-5540-b1c8-a88a73b9d63e | [
false,
true
] | [
"<think>\n嗯，好的，我现在要解决这个数学题。题目是说，给定a=0.5，b=1/3，那么a-b等于1/78的某个倍数，问这个倍数是多少。对吧？题目里可能有些翻译上的问题，我需要仔细理解。\n\n首先，题目里的“times”应该是指“**** **** **** **** ****\n\n",
"<think>\n嗯，好的，我现在要解决这个问题。题目是说，给定a=0.5，b=1/3，然后a减b是某个数的1/78倍，我需要找到那个数。题目这里可能翻译得有点问题，不过大概就是这个意思。首先我需要理清楚题目的结构。\n\n首先，题目给出a=0.5和b=1/3，然后计算a - b的结果，这个结果等于某个数的1/78倍。换句... | [
false,
true
] | null | null | 1 | [
{
"content": "2. (5 points) Given $a=0.5, b=\\frac{1}{3}$, then $a-b$ is $\\frac{1}{78}$ of $\\qquad$ times\n\n保留源文本的换行和格式，翻译结果如下：\n\n2. (5 points) Given $a=0.5, b=\\frac{1}{3}$, then $a-b$ is $\\frac{1}{78}$ of $\\qquad$ times",
"role": "user"
},
{
"content": "<think>\n嗯，好的，我现在要解决这个问题。题目是说，给定a=0.5，... | <think>
嗯，好的，我现在要解决这个问题。题目是说，给定a=0.5，b=1/3，然后a减b是某个数的1/78倍，我需要找到那个数。题目这里可能翻译得有点问题，不过大概就是这个意思。首先我需要理清楚题目的结构。
首先，题目给出a=0.5和b=1/3，然后计算a - b的结果，这个结果等于某个数的1/78倍。换句话说，就是a - b = (1/78) × x，这里x就是题目中需要填的那个数。我的任务就是找到这个x的值。
首先，我应该先计算a - b的值。a是0.5，也就是1/2，而b是1/3。所以，a - b就是1/2 - 1/3。这时候，我需要找到这两个分数的公共分母，公共分母应该是6。因此，1/2等于3/6，1/3等于2/... | 1,660 | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
2. (5 points) Given $a=0.5, b=\frac{1}{3}$, then $a-b$ is $\frac{1}{78}$ of $\qquad$ times
保留源文本的换行和格式，翻译结果如下：
2. (5 points) Given $a=0.5, b=\frac{1}{3}$, then $a-b$ is $\frac{1}{78}$ of $\qquad$ times<|... |
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