In a girl's basketball game, Brooklyn scored 56 points from 2-pointers and 3-pointers.
Her father in the stands remarked that she made twice as many 2-pointers as 3-pointers during the game.
How many of each did she make?
let w = two pointers ... and ... h = three pointers
w = 2 h
2 w + 3 h = 56
substituting ... 2 (2 h) + 3 h = 56 ... 7 h = 56
solve for h , then substitute back to find w
Well, it seems like Brooklyn really loves using her "two"-cchi moves! Her father's observation hints that she made twice as many 2-pointers as 3-pointers. Let's put that into practice with some math-juggling!
Let's say Brooklyn made "x" 3-pointers during the game. Since her father said she made twice as many 2-pointers, that means she made 2x 2-pointers.
So, the total points Brooklyn scored from 2-pointers would be 2x points, and the total points she scored from 3-pointers would be 3x points.
Now, we know that the total points Brooklyn scored from both types of shots sum up to 56 points. Therefore, we can create an equation:
2x + 3x = 56.
Combining like terms, we get:
5x = 56.
Now, when we divide both sides of the equation by 5, we find that x = 11.2. However, we can't have a fraction of a shot, so we'll need to round down to the nearest whole number.
Therefore, Brooklyn made 11 shots from the 3-point line and twice as many, which is 22 shots, from the 2-point line.
So, Brooklyn made 11 shots from downtown and 22 from the inside – pretty impressive basketball skills!
Let's assume the number of 2-pointers made by Brooklyn is x and the number of 3-pointers made is y.
According to the problem, Brooklyn scored 56 points in total:
2-pointers = x
3-pointers = y
The number of points scored from 2-pointers is calculated by multiplying the number of 2-pointers made by 2, and the number of points scored from 3-pointers is calculated by multiplying the number of 3-pointers made by 3:
Total points = 2 * (x) + 3 * (y)
The problem states that Brooklyn made twice as many 2-pointers as 3-pointers:
x = 2 * y
Substituting the value of x in the equation for total points:
2 * (2 * y) + 3 * (y) = 56
Simplifying the equation:
4y + 3y = 56
7y = 56
y = 8
Substituting the value of y in the equation for x:
x = 2 * 8
x = 16
Therefore, Brooklyn made 16 2-pointers and 8 3-pointers in the game.
To solve this problem, let's assign variables to the unknowns.
Let's say the number of 2-pointers Brooklyn made is 'x', and the number of 3-pointers she made is 'y'.
According to the problem, Brooklyn scored a total of 56 points, combining both 2-pointers and 3-pointers. Since each 2-pointer is worth 2 points and each 3-pointer is worth 3 points, we can create an equation to express this relationship:
2x + 3y = 56
The problem also states that Brooklyn made twice as many 2-pointers as 3-pointers. In other words, the value of 'x' is twice the value of 'y'. So we can write another equation:
x = 2y
Now we have a system of two equations:
2x + 3y = 56 (Equation 1)
x = 2y (Equation 2)
We can solve this system of equations using substitution or elimination method.
Let's use substitution method here:
Substitute the value of 'x' from Equation 2 into Equation 1:
2(2y) + 3y = 56
Simplify:
4y + 3y = 56
7y = 56
y = 8
Now substitute the value of 'y' into Equation 2 to find 'x':
x = 2(8)
x = 16
Therefore, Brooklyn made 16 two-pointers and 8 three-pointers during the game.