1. Clay is on the basketball team at his high school. In one game, he had a total of 20 points, made up of 2-point and 3-point baskets. If he made a total of 9 baskets, how many of each type shot did he make?
Since 20 is an even number, there must be an even number of 3-point baskets.
2 3-point and 7 2-point baskets.
To find out how many of each type of shot Clay made, we can set up a system of equations based on the given information.
Let's say Clay made x 2-point baskets and y 3-point baskets.
From the given information, we know that:
x + y = 9 (equation 1) -- since Clay made a total of 9 baskets
2x + 3y = 20 (equation 2) -- since the total points he scored was 20
To solve this system of equations, you can use either substitution or elimination method.
Let's use the elimination method in this case:
First, multiply equation 1 by 2 to make the coefficient of x in both equations the same:
2(x + y) = 2(9)
2x + 2y = 18 (equation 3)
Now, subtract equation 3 from equation 2 to eliminate the x variable:
(2x + 3y) - (2x + 2y) = 20 - 18
2x - 2x + 3y - 2y = 2
y = 2
Now that we have the value of y, we can substitute it back into equation 1 to solve for x:
x + (2) = 9
x + 2 = 9
x = 9 - 2
x = 7
So Clay made 7 2-point baskets and 2 3-point baskets in the game.