problem stringlengths 10 5.15k | answer stringlengths 0 1.23k |
|---|---|
Express $\frac{37}{80}$ as a terminating decimal. | 0.4625 |
Find the area of the circle defined by \(x^2 + 4x + y^2 + 10y + 13 = 0\) that lies above the line \(y = -2\). | 2\pi |
The dinner bill for 6 friends came to $150. Silas said he would pay for half of the bill and the remaining friends could split the rest of the bill and leave a 10% tip for the whole meal. How many dollars will one of the friends pay? | Silas paid half = 150/2 = <<150/2=75>>75
Remaining bill paid by 5 friends = 75 + 10% of 150 = 75 + 15 = 90
Each person will pay 1/5 which is 90/5 = <<90/5=18>>18
Each friend will pay $<<18=18>>18.
#### 18 |
Xiao Ming, Xiao Hong, and Xiao Gang are three people whose ages are three consecutive even numbers. Their total age is 48 years old. What is the youngest age? What is the oldest age? | 18 |
The area of the largest regular hexagon that can fit inside of a rectangle with side lengths 20 and 22 can be expressed as $a \sqrt{b}-c$, for positive integers $a, b$, and $c$, where $b$ is squarefree. Compute $100 a+10 b+c$. | 134610 |
John buys 3 reels of 100m fishing line. He cuts it into 10m sections. How many sections does he get? | He buys 3*100=<<3*100=300>>300m
So he gets 300/10=<<300/10=30>>30 sections
#### 30 |
Find $a$ if the remainder is constant when $10x^3-7x^2+ax+6$ is divided by $2x^2-3x+1$. | -7 |
In multiplying two positive integers $a$ and $b$, Ron reversed the digits of the two-digit number $a$. His erroneous product was $161$. What is the correct value of the product of $a$ and $b$? | 224 |
At a school cafeteria, Sam wants to buy a lunch consisting of one main dish, one beverage, and one snack. The table below lists Sam's choices in the cafeteria. How many distinct possible lunches can he buy if he avoids pairing Fish and Chips with Soda due to dietary restrictions?
\begin{tabular}{ |c | c | c | }
\hline... | 14 |
Given a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ ($a>0, b>0$) with a point C on it, a line passing through the center of the hyperbola intersects the hyperbola at points A and B. Let the slopes of the lines AC and BC be $k_1$ and $k_2$ respectively. Find the eccentricity of the hyperbola when $\frac{2}{k_1 k_2... | \sqrt{3} |
In the diagram, \( B, C \) and \( D \) lie on a straight line, with \(\angle ACD=100^{\circ}\), \(\angle ADB=x^{\circ}\), \(\angle ABD=2x^{\circ}\), and \(\angle DAC=\angle BAC=y^{\circ}\). The value of \( x \) is: | 20 |
Calculate the value of $\frac{1}{2 + \frac{1}{3 + \frac{1}{4}}}$. | \frac{13}{30} |
Tyrone had $97$ marbles and Eric had $11$ marbles. Tyrone then gave some of his marbles to Eric so that Tyrone ended with twice as many marbles as Eric. How many marbles did Tyrone give to Eric? | 18 |
Given the function $f(x)=3\sin(2x-\frac{π}{3})-2\cos^{2}(x-\frac{π}{6})+1$, the graph of function $f(x)$ is shifted to the left by $\frac{π}{6}$ units, resulting in the graph of function $g(x)$. Find $\sin (2x_{1}+2x_{2})$, where $x_{1}$ and $x_{2}$ are the two roots of the equation $g(x)=a$ in the interval $[0,\frac{π... | -\frac{3}{5} |
Given that $\frac{\cos \alpha + \sin \alpha}{\cos \alpha - \sin \alpha} = 2$, find the value of $\frac{1 + \sin 4\alpha - \cos 4\alpha}{1 + \sin 4\alpha + \cos 4\alpha}$. | \frac{3}{4} |
Consider the following pair of equations:
\[120x^4 + ax^3 + bx^2 + cx + 18 = 0\] and
\[18x^5 + dx^4 + ex^3 + fx^2 + gx + 120 = 0\]
These equations have a common rational root $k$ which is not an integer and is positive. Determine $k$. | \frac{1}{2} |
The storage capacity of two reservoirs, A and B, changes over time. The relationship between the storage capacity of reservoir A (in hundred tons) and time $t$ (in hours) is: $f(t) = 2 + \sin t$, where $t \in [0, 12]$. The relationship between the storage capacity of reservoir B (in hundred tons) and time $t$ (in hours... | 6.721 |
Given that the polynomial \(x^2 - kx + 24\) has only positive integer roots, find the average of all distinct possibilities for \(k\). | 15 |
Determine the smallest positive integer $n$, different from 2004, such that there exists a polynomial $f(x)$ with integer coefficients for which the equation $f(x) = 2004$ has at least one integer solution and the equation $f(x) = n$ has at least 2004 different integer solutions. | (1002!)^2 + 2004 |
Let $f(x)=-3x^2+x-4$, $g(x)=-5x^2+3x-8$, and $h(x)=5x^2+5x+1$. Express $f(x)+g(x)+h(x)$ as a single polynomial, with the terms in order by decreasing degree. | -3x^2 +9x -11 |
James is standing at the point $(0,1)$ on the coordinate plane and wants to eat a hamburger. For each integer $n \geq 0$, the point $(n, 0)$ has a hamburger with $n$ patties. There is also a wall at $y=2.1$ which James cannot cross. In each move, James can go either up, right, or down 1 unit as long as he does not cros... | \frac{7}{3} |
Calculate
\[T = \sum \frac{1}{n_1! \cdot n_2! \cdot \cdots n_{1994}! \cdot (n_2 + 2 \cdot n_3 + 3 \cdot n_4 + \ldots + 1993 \cdot n_{1994})!}\]
where the sum is taken over all 1994-tuples of the numbers $n_1, n_2, \ldots, n_{1994} \in \mathbb{N} \cup \{0\}$ satisfying $n_1 + 2 \cdot n_2 + 3 \cdot n_3 + \ldots... | \frac{1}{1994!} |
Given three distinct points $A$, $B$, $C$ on a straight line, and $\overrightarrow{OB}=a_{5} \overrightarrow{OA}+a_{2012} \overrightarrow{OC}$, find the sum of the first 2016 terms of the arithmetic sequence $\{a_{n}\}$. | 1008 |
Given $sin( \frac {\pi}{6}-\alpha)-cos\alpha= \frac {1}{3}$, find $cos(2\alpha+ \frac {\pi}{3})$. | \frac {7}{9} |
Codger is a three-footed sloth. He has a challenging time buying shoes because the stores only sell the shoes in pairs. If he already owns the 3-piece set of shoes he is wearing, how many pairs of shoes does he need to buy to have 5 complete 3-piece sets of shoes? | To have five 3-piece sets, he needs to have a total of 5*3=<<5*3=15>>15 shoes,
If he already owns three shoes, then he needs to buy 15-3=<<15-3=12>>12 additional shoes.
Since each pair of shoes includes two shoes, he needs to buy a total of 12/2=<<12/2=6>>6 pairs of shoes.
#### 6 |
A right circular cone has a base with radius $600$ and height $200\sqrt{7}.$ A fly starts at a point on the surface of the cone whose distance from the vertex of the cone is $125$, and crawls along the surface of the cone to a point on the exact opposite side of the cone whose distance from the vertex is $375\sqrt{2}.$... | 625 |
Let $f(x) = x^2 + ax + b$ and $g(x) = x^2 + cx + d$ be two distinct polynomials with real coefficients such that the $x$-coordinate of the vertex of $f$ is a root of $g,$ and the $x$-coordinate of the vertex of $g$ is a root of $f,$ and both $f$ and $g$ have the same minimum value. If the graphs of the two polynomials... | -400 |
Triangle $ABC$ is an isosceles right triangle with the measure of angle $A$ equal to 90 degrees. The length of segment $AC$ is 6 cm. What is the area of triangle $ABC$, in square centimeters? | 18 |
Two sectors of a circle of radius $15$ overlap in the same manner as the original problem, with $P$ and $R$ as the centers of the respective circles. The angle at the centers for both sectors is now $45^\circ$. Determine the area of the shaded region. | \frac{225\pi - 450\sqrt{2}}{4} |
To arrange 5 volunteers and 2 elderly people in a row, where the 2 elderly people are adjacent but not at the ends, calculate the total number of different arrangements. | 960 |
How many equilateral hexagons of side length $\sqrt{13}$ have one vertex at $(0,0)$ and the other five vertices at lattice points? (A lattice point is a point whose Cartesian coordinates are both integers. A hexagon may be concave but not self-intersecting.) | 216 |
Real numbers $x$ and $y$ are chosen independently and uniformly at random from the interval $(0,1)$. What is the probability that $\lfloor\log_2x\rfloor=\lfloor\log_2y\rfloor$? | \frac{1}{3} |
Given that $8^{-1} \equiv 85 \pmod{97}$, find $64^{-1} \pmod{97}$, as a residue modulo 97. (Give an answer between 0 and 96, inclusive.) | 47 |
The number $947$ can be written as $23q + r$ where $q$ and $r$ are positive integers. What is the greatest possible value of $q - r$? | 37 |
Compute $54 \times 46$ in your head. | 2484 |
In $\triangle ABC$, it is known that $\cos A=\frac{4}{5}$ and $\tan (A-B)=-\frac{1}{2}$. Find the value of $\tan C$. | \frac{11}{2} |
What is the number of units in the distance between $(2,5)$ and $(-6,-1)$? | 10 |
Find all real solutions to $x^{4}+(2-x)^{4}=34$. | 1 \pm \sqrt{2} |
A jug needs 40 cups of water to be full. A custodian at Truman Elementary School has to fill water jugs for 200 students, who drink 10 cups of water in a day. How many water jugs will the custodian fill with cups of water to provide the students with all the water they need in a day? | Since each student needs 10 cups of water per day and there are 200 students, the custodian has to provide 200*10 = <<200*10=2000>>2000 cups of water.
A jug of water needs 40 cups to be full, so 2000 cups of water will fill 2000/40 = <<2000/40=50>>50 jugs
#### 50 |
Let $L,E,T,M,$ and $O$ be digits that satisfy $LEET+LMT=TOOL.$ Given that $O$ has the value of $0,$ digits may be repeated, and $L\neq0,$ what is the value of the $4$ -digit integer $ELMO?$ | 1880 |
What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers? | 5 |
A line of soldiers 1 mile long is jogging. The drill sergeant, in a car, moving at twice their speed, repeatedly drives from the back of the line to the front of the line and back again. When each soldier has marched 15 miles, how much mileage has been added to the car, to the nearest mile? | 30 |
What is the sum of the odd positive integers less than 50? | 625 |
Given that $\cos \theta = \frac{12}{13}, \theta \in \left( \pi, 2\pi \right)$, find the values of $\sin \left( \theta - \frac{\pi}{6} \right)$ and $\tan \left( \theta + \frac{\pi}{4} \right)$. | \frac{7}{17} |
Given $f(x) = ax^3 + bx^9 + 2$ has a maximum value of 5 on the interval $(0, +\infty)$, find the minimum value of $f(x)$ on the interval $(-\infty, 0)$. | -1 |
Given the function $f(x)=\sin x\cos x-\cos ^{2}x$.
$(1)$ Find the interval where $f(x)$ is decreasing.
$(2)$ Let the zeros of $f(x)$ on $(0,+\infty)$ be arranged in ascending order to form a sequence $\{a_{n}\}$. Find the sum of the first $10$ terms of $\{a_{n}\}$. | \frac{95\pi}{4} |
We wrote letters to ten of our friends and randomly placed the letters into addressed envelopes. What is the probability that exactly 5 letters will end up with their intended recipients? | 0.0031 |
What is the smallest positive integer with six positive odd integer divisors and twelve positive even integer divisors? | 180 |
The polynomial sequence is defined as follows: \( f_{0}(x)=1 \) and \( f_{n+1}(x)=\left(x^{2}-1\right) f_{n}(x)-2x \) for \( n=0,1,2, \ldots \). Find the sum of the absolute values of the coefficients of \( f_{6}(x) \). | 190 |
Assume that the probability of a certain athlete hitting the bullseye with a dart is $40\%$. Now, the probability that the athlete hits the bullseye exactly once in two dart throws is estimated using a random simulation method: first, a random integer value between $0$ and $9$ is generated by a calculator, where $1$, $... | 0.5 |
Distinct prime numbers $p, q, r$ satisfy the equation $2 p q r+50 p q=7 p q r+55 p r=8 p q r+12 q r=A$ for some positive integer $A$. What is $A$ ? | 1980 |
Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle? | 8 |
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is $m$ times the area of the square. What is the ratio of the area of the other smal... | \frac{1}{4m} |
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three factors, the probability t... | 76 |
In the diagram, \( AB \) and \( CD \) intersect at \( E \). If \(\triangle BCE\) is equilateral and \(\triangle ADE\) is a right-angled triangle, what is the value of \( x \)? | 30 |
In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, and it is given that $2c-2a\cos B=b$.
$(1)$ Find the size of angle $A$;
$(2)$ If the area of $\triangle ABC$ is $\frac{\sqrt{3}}{4}$, and $c^{2}+ab\cos C+a^{2}=4$, find $a$. | \frac{\sqrt{7}}{2} |
In a pot, there are 6 sesame-filled dumplings, 5 peanut-filled dumplings, and 4 red bean paste-filled dumplings. These three types of dumplings look exactly the same from the outside. If 4 dumplings are randomly scooped out, the probability that at least one dumpling of each type is scooped out is ______. | \dfrac{48}{91} |
Find the intercept on the $x$-axis of the line that is perpendicular to the line $3x-4y-7=0$ and forms a triangle with both coordinate axes having an area of $6$. | -3 |
Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining die? | \frac{5}{24} |
Convert the complex number \(1 + i \sqrt{3}\) into its exponential form \(re^{i \theta}\) and find \(\theta\). | \frac{\pi}{3} |
Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that
\[f(x) f(y) - f(xy) = x + y\]for all real numbers $x$ and $y.$
Let $n$ be the number of possible values of $f(2),$ and let $s$ be the sum of all possible values of $f(2).$ Find $n \times s.$ | 3 |
Let $\mathcal{P}$ be the parabola given by the equation \( y = x^2 \). Suppose a circle $\mathcal{C}$ intersects $\mathcal{P}$ at four distinct points. If three of these points are \((-4,16)\), \((1,1)\), and \((6,36)\), find the sum of the distances from the directrix of the parabola to all four intersection points. | 63 |
What is the smallest five-digit positive integer congruent to $2 \pmod{17}$? | 10013 |
The numbers from 1 to 200, inclusive, are placed in a bag. A number is randomly selected from the bag. What is the probability that it is neither a perfect square, a perfect cube, nor a multiple of 7? Express your answer as a common fraction. | \frac{39}{50} |
There are real numbers $a, b, c, d$ such that for all $(x, y)$ satisfying $6y^2 = 2x^3 + 3x^2 + x$ , if $x_1 = ax + b$ and $y_1 = cy + d$ , then $y_1^2 = x_1^3 - 36x_1$ . What is $a + b + c + d$ ? | 90 |
Let $\pi$ be a permutation of the numbers from 1 through 2012. What is the maximum possible number of integers $n$ with $1 \leq n \leq 2011$ such that $\pi(n)$ divides $\pi(n+1)$? | 1006 |
Compute the value of $k$ such that the equation
\[\frac{x + 2}{kx - 1} = x\]has exactly one solution. | 0 |
Find the sum of the roots of the equation \[(2x^3 + x^2 - 8x + 20)(5x^3 - 25x^2 + 19) = 0.\] | \tfrac{9}{2} |
Two people are playing "Easter egg battle." In front of them is a large basket of eggs. They randomly pick one egg each and hit them against each other. One of the eggs breaks, the defeated player takes a new egg, and the winner keeps their egg for the next round (the outcome of each round depends only on which egg has... | 11/12 |
Yura has a calculator that allows multiplying a number by 3, adding 3 to a number, or (if the number is divisible by 3) dividing by 3. How can you obtain the number 11 from the number 1 using this calculator? | 11 |
A coin is tossed 10 times. Find the probability that no two heads appear consecutively. | 9/64 |
Define
\[ A' = \frac{1}{1^2} + \frac{1}{7^2} - \frac{1}{11^2} - \frac{1}{13^2} + \frac{1}{19^2} + \frac{1}{23^2} - \dotsb, \]
which omits all terms of the form $\frac{1}{n^2}$ where $n$ is an odd multiple of 5, and
\[ B' = \frac{1}{5^2} - \frac{1}{25^2} + \frac{1}{35^2} - \frac{1}{55^2} + \frac{1}{65^2} - \frac{1}{85^2... | 26 |
Three balls marked $1,2$ and $3$ are placed in an urn. One ball is drawn, its number is recorded, and then the ball is returned to the urn. This process is repeated and then repeated once more, and each ball is equally likely to be drawn on each occasion. If the sum of the numbers recorded is $6$, what is the probabili... | \frac{1}{7} |
One day while Tony plays in the back yard of the Kubik's home, he wonders about the width of the back yard, which is in the shape of a rectangle. A row of trees spans the width of the back of the yard by the fence, and Tony realizes that all the trees have almost exactly the same diameter, and the trees look equally s... | 82 |
Let $a\star b = a^b+ab$. If $a$ and $b$ are positive integers greater than or equal to 2 and $a\star b =15$, find $a+b$. | 5 |
Cars A and B travel the same distance. Car A travels half that distance at $u$ miles per hour and half at $v$ miles per hour. Car B travels half the time at $u$ miles per hour and half at $v$ miles per hour. The average speed of Car A is $x$ miles per hour and that of Car B is $y$ miles per hour. Then we always have | $x \leq y$ |
If the area of $\triangle ABC$ is $64$ square units and the geometric mean (mean proportional) between sides $AB$ and $AC$ is $12$ inches, then $\sin A$ is equal to | \frac{8}{9} |
Three circles with radii 2, 3, and 10 units are placed inside a larger circle such that all circles are touching one another. Determine the value of the radius of the larger circle. | 15 |
What is the largest value among $\operatorname{lcm}[12,2],$ $\operatorname{lcm}[12,4],$ $\operatorname{lcm}[12,6],$ $\operatorname{lcm}[12,8],$ $\operatorname{lcm}[12,10],$ and $\operatorname{lcm}[12,12]?$ Express your answer as an integer. | 60 |
Find the ordered pair $(a,b)$ of integers such that
\[\sqrt{9 - 8 \sin 50^\circ} = a + b \csc 50^\circ.\] | (3,-1) |
Andrey found the product of all the numbers from 1 to 11 inclusive and wrote the result on the board. During a break, someone accidentally erased three digits, leaving the number $399 * 68 * *$. Help restore the missing digits without recalculating the product. | 39916800 |
Chalktown High School had their prom last weekend. There were 123 students who attended. If 3 students attended on their own, how many couples came to the prom? | There were 123 students – 3 single attendees = <<123-3=120>>120 students in couples.
120 students / 2 in a couple = <<120/2=60>>60 couples.
#### 60 |
The sixth graders were discussing how old their principal is. Anya said, "He is older than 38 years." Borya said, "He is younger than 35 years." Vova: "He is younger than 40 years." Galya: "He is older than 40 years." Dima: "Borya and Vova are right." Sasha: "You are all wrong." It turned out that the boys and girls we... | 39 |
Point $Q$ lies on the diagonal $AC$ of square $EFGH$ with $EQ > GQ$. Let $R_{1}$ and $R_{2}$ be the circumcenters of triangles $EFQ$ and $GHQ$ respectively. Given that $EF = 8$ and $\angle R_{1}QR_{2} = 90^{\circ}$, find the length $EQ$ in the form $\sqrt{c} + \sqrt{d}$, where $c$ and $d$ are positive integers. Find $c... | 40 |
Given that real numbers x and y satisfy x + y = 5 and x * y = -3, find the value of x + x^4 / y^3 + y^4 / x^3 + y. | 5 + \frac{2829}{27} |
Given an arithmetic sequence $\{a_n\}$ with common difference $d \neq 0$, and its first term $a_1 = d$. The sum of the first $n$ terms of the sequence $\{a_n^2\}$ is denoted as $S_n$. Additionally, there is a geometric sequence $\{b_n\}$ with a common ratio $q$ that is a positive rational number less than $1$. The firs... | \frac{1}{2} |
Let $T$ be the set of ordered triples $(x,y,z)$, where $x,y,z$ are integers with $0\leq x,y,z\leq9$. Players $A$ and $B$ play the following guessing game. Player $A$ chooses a triple $(x,y,z)$ in $T$, and Player $B$ has to discover $A$[i]'s[/i] triple in as few moves as possible. A [i]move[/i] consists of the followin... | 3 |
How many distinct prime factors does 56 have? | 2 |
The faces of an octahedral die are labeled with digits $1$ through $8$. What is the probability, expressed as a common fraction, of rolling a sum of $15$ with a pair of such octahedral dice? | \frac{1}{32} |
In how many ways can you rearrange the letters of ‘Alejandro’ such that it contains one of the words ‘ned’ or ‘den’? | 40320 |
A 9 by 9 checkerboard has alternating black and white squares. How many distinct squares, with sides on the grid lines of the checkerboard (horizontal and vertical) and containing at least 6 black squares, can be drawn on the checkerboard? | 91 |
James has to refuel his plane. It used to cost $200 to refill the tank. He got an extra tank to double fuel capacity. Fuel prices also went up by 20%. How much does he pay now for fuel? | The cost to fill a tank went up 200*.2=$<<200*.2=40>>40
So it cost 200+40=$<<200+40=240>>240 to fill the tank
That means he now pays 240*2=$<<240*2=480>>480
#### 480 |
Hasan is packing up his apartment because he’s moving across the country for a new job. He needs to ship several boxes to his new home. The movers have asked that Hasan avoid putting more than a certain weight in pounds in any cardboard box. The moving company has helpfully provided Hasan with a digital scale that will... | Let x be the number of plates removed from the box.
Hasan figured out the movers' weight limit was 20 pounds. Since a pound is equal to 16 ounces, each box can hold 20 * 16, or <<20*16=320>>320 ounces.
Each plate weighs 10 ounces, so the weight of the plates in the box after Hasan removes enough plates to satisfy the m... |
Before the soccer match between the "North" and "South" teams, five predictions were made:
a) There will be no draw;
b) "South" will concede goals;
c) "North" will win;
d) "North" will not lose;
e) Exactly 3 goals will be scored in the match.
After the match, it was found that exactly three predictions were corre... | 2-1 |
John's pool is 5 feet deeper than 2 times Sarah’s pool. If John’s pool is 15 feet deep, how deep is Sarah’s pool? | Let x be the number of feet in John’s pool
2*x + 5=15
2x=10
x=<<5=5>>5
#### 5 |
Find the quadratic function $f(x) = x^2 + ax + b$ such that
\[\frac{f(f(x) + x)}{f(x)} = x^2 + 1776x + 2010.\] | x^2 + 1774x + 235 |
Isabella uses one-foot cubical blocks to build a rectangular fort that is $12$ feet long, $10$ feet wide, and $5$ feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain? | 280 |
Jane plans on reading a novel she borrows from her friend. She reads twice a day, once in the morning and once in the evening. In the morning she reads 5 pages and in the evening she reads 10 pages. If she reads at this rate for a week, how many pages will she read? | The number of pages Jane reads in a day is 5 in the morning and 10 in the evening, so she reads 10 + 5 = <<10+5=15>>15 pages in a day.
If she reads for a week she reads for 7 days, so by the end of the week she reads 15 * 7 = <<15*7=105>>105 pages.
#### 105 |
Given a point P on the curve $y = x^2 - \ln x$, find the minimum distance from point P to the line $y = x + 2$. | \sqrt{2} |
In his first season at Best Hockey's team, Louie scored four goals in the last hockey match of this season. His brother has scored twice as many goals as Louie scored in the last match in each game he's played in each of the three seasons he's been on the team. Each season has 50 games. What is the total number of goa... | If Louie scored 4 goals last night, his brother has scored 2 * 4 goals = <<4*2=8>>8 goals in each game
The total number of games Louie's brother has played in is 3 seasons * 50 games/season = <<3*50=150>>150 games
Louie's brother's total number of goals in the three seasons is 8 goals/game * 150 games = <<8*150=1200>>1... |
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