Question

At a basketball​ game, a team made 52 successful shots. They were a combination of​ 1- and​ 2-point shots. The team scored 89 points in all. Write and solve a system of equations to find the number of each type of shot.

Answer 1

• 15 1-point shots
• 37 2-point shots

Explanation:

You want a system of equations and their solution for the number of shots of each type if the total number is 52 and the points from 1- and 2-point shots total 89.

Setup

Let x and y represent the numbers of 1- and 2-point shots, respectively. The problem description tells of two relations:

x + y = 52 . . . . . . . total of shots is 52

x + 2y = 89 . . . . . . total of points is 89

Solution

Subtracting the first equation from the second, we get ...

(x +2y) -(x +y) - (89) -(52)

y = 37

Then the first equation tells us ...

x = 52 -y = 52 -37 = 15

The team made 15 1-point shots and 37 2-point shots.