Question

A basketball team recently scored a total of 98 points on a combination of 2-point field goals, 3-point field goals, and 1-point foul shots. Altogether, the team made 56 baskets and 16 more 2-pointers than foul shots. How many shots of each kind were made? How many 1-point foul shots did the team make? How many 2.point field goals did the team make? How many 3-point field goals did the team make?

Answer 1

let 1 point foul shots = x

2 point goals = y

3 point goal = z

x + y + z = 56

x + 2y + 3z = 98

y = x + 16

solving the equations

Multiply first equation by -1 and add the result to the second equation. The result is: x + y + z = + y + 2z = -12 + y Multiply first equation by 1 and add the result to the third equation. The result is: x + y + z = + y + 2 z = + 2y + z = 72 Multiply second equation by-2 and add the result to the third equation. The result is: x + y + z = 56 + y + 2z = 42 – 3 z = – 12 solve for z. -32= -12 2=4 solve for y. y + 2z = 42 y+2.4 = 42 y=34

x = 18

1 point foul = 18

2 point goals = 34

3 point goals = 4