instruction stringclasses 9
values | response stringclasses 9
values |
|---|---|
A farmer has a certain number of apples. He gives away 30% of his apples to his neighbor and then realizes he still has 140 apples left. How many apples did the farmer originally have? Show your work. | Let's denote the original number of apples as x. According to the problem, after giving away 30% of his apples, he is left with 140 apples. This means that he kept 70% of his apples. We can express this mathematically:
0.7x = 140.
To find x, we divide both sides by 0.7:
x = 140 / 0.7 = 200.
Thus, the farmer origin... |
In a class of students, 60% are girls. If there are 24 boys in the class, how many students are there in total? Provide detailed reasoning. | Let the total number of students be y. Since 60% of the students are girls, it follows that 40% must be boys. Therefore, we can set up the equation based on the information given:
0.4y = 24 (since there are 24 boys).
Now, to solve for y, we divide both sides by 0.4:
y = 24 / 0.4 = 60.
So, the total number of studen... |
A bookstore sells novels at $15 each and textbooks at $25 each. If a customer buys a total of 10 books for $200, how many novels did they buy? Explain your thought process step-by-step. | Let n represent the number of novels and t represent the number of textbooks. We know two things from the problem:
1. The total number of books bought is 10: n + t = 10.
2. The total cost of the books is $200: 15n + 25t = 200.
We can solve these equations simultaneously. From the first equation, we can express t in te... |
A box contains red, blue, and green marbles in the ratio of 3:4:5 respectively. If there are 36 marbles in total, how many red marbles are there? Show your calculations clearly. | Let the number of red marbles be represented as 3x, blue marbles as 4x, and green marbles as 5x. The total number of marbles can be expressed as:
3x + 4x + 5x = 12x.
According to the problem, the total number of marbles is 36:
12x = 36.
To find x, we divide both sides by 12:
x = 36 / 12 = 3.
Now, substituting back t... |
If a company produces 500 gadgets per day and increases production by 20% every month, how many gadgets will it produce after three months? Provide a step-by-step explanation. | Initially, the company produces 500 gadgets. Each month, production increases by 20%. To calculate the production over three months, we can use the formula for compound growth:
After 1 month: Production = 500 * (1 + 0.20) = 500 * 1.20 = 600 gadgets.
After 2 months: Production = 600 * (1 + 0.20) = 600 * 1.20 = 720 gad... |
A recipe requires 2 cups of flour for every 3 cups of sugar. If you want to make a batch using 12 cups of sugar, how much flour do you need? Show your reasoning. | The ratio of flour to sugar in the recipe is 2:3. This means for every 3 cups of sugar, you need 2 cups of flour. To find out how much flour is needed for 12 cups of sugar, we can set up a proportion:
Let f be the amount of flour needed. Then:
2/3 = f/12.
Cross-multiplying gives:
2 * 12 = 3f,
which simplifies to:
24 ... |
A train leaves a station traveling north at a speed of 80 km/h. At the same time, another train leaves the same station traveling south at a speed of 100 km/h. How far apart will the trains be after 2 hours? Explain your steps clearly. | Both trains leave the station at the same time but travel in opposite directions. After 2 hours, we can calculate the distance traveled by each train separately:
For the northbound train:
Distance = Speed 脳 Time = 80 km/h 脳 2 h = 160 km.
For the southbound train:
Distance = Speed 脳 Time = 100 km/h 脳 2 h = 200 km.
To... |
In a family, the father is twice as old as the son. In 10 years, the father's age will be 1.5 times the son's age. What are their current ages? Provide a detailed solution. | Let the current age of the son be s. Then, the father's current age would be 2s (since he is twice as old). In 10 years, the son's age will be s + 10, and the father's age will be 2s + 10. According to the problem, in 10 years, the father's age will be 1.5 times the son's age:
2s + 10 = 1.5(s + 10).
Expanding the rig... |
A group of friends decides to share the cost of a pizza equally. If the pizza costs $18 and there are 6 friends sharing it, how much does each friend pay? Include your calculation steps. | To determine how much each friend pays, we start with the total cost of the pizza, which is $18. Since there are 6 friends sharing the cost equally, we can calculate the amount each friend pays by dividing the total cost by the number of friends:
Amount each friend pays = Total cost / Number of friends = $18 / 6.
Cal... |
README.md exists but content is empty.
- Downloads last month
- 2