Mandy scored 22 points in a basketball game. If she made 9 field goals, worth either 2 or 4 points, and no free throws, how many three-point field goals did she make?
Didn't know baskets were worth 4 point, did you mean 2 or 3 points?
I will assume that.
number of 2-pointers ---x
number of 3-pointers --- 9
2x + 3(9-x) = 22
2x + 27 - 3x = 22
x = 5
so 5 two-pointers and 4 three-pointers
check"
5(2) + 4(3) = 22
To find out how many three-point field goals Mandy made, we first need to determine the number of 2-point field goals and 4-point field goals she made.
Let's assume that Mandy made x number of 2-point field goals and y number of 4-point field goals.
Since each 2-point field goal contributes 2 points to her total score, the total value of all 2-point field goals made would be 2x. Likewise, each 4-point field goal contributes 4 points to her total score, so the total value of all 4-point field goals made would be 4y.
According to the information given, Mandy made a total of 9 field goals. So we have the equation:
x + y = 9 (Equation 1)
Also, her total score from field goals was 22 points. Using the values we defined earlier, the equation for the total score becomes:
2x + 4y = 22 (Equation 2)
We can now solve this system of equations to find the values of x and y, and thus determine the number of 2-point and 4-point field goals.
First, let's solve Equation 1 for one variable (e.g., x):
x = 9 - y
Substitute this value of x into Equation 2:
2(9 - y) + 4y = 22
Simplify the equation:
18 - 2y + 4y = 22
2y = 4
Solve for y:
y = 2
Now substitute this value back into Equation 1 to find x:
x + 2 = 9
x = 7
Therefore, Mandy made 7 two-point field goals and 2 four-point field goals. To find the number of three-point field goals, subtract these values from the total number of field goals:
Total field goals = 7 + 2 = 9
Number of three-point field goals = Total field goals - (Number of 2-point field goals + Number of 4-point field goals)
Number of three-point field goals = 9 - (7 + 2) = 9 - 9 = 0
Hence, Mandy did not make any three-point field goals in the game.