Question

A basketball team recently scored a total of 95 points on a combination of​ 2-point field​ goals, 3-point field​ goals, and​ 1-point foul shots.​ Altogether, the team made 53 baskets and 13 more​ 2-pointers than foul shots. How many shots of each kind were​ made?

Answer 1

We know that a minimum of 14 2-pointers have to be made to have at least 1-point shot. So we can calculate the total points with the 14 2-pointers (hint: 14x2).

We know that 53 baskets were made and out of that at least 14 were 2 pointers and 1 was one pointer. That leaves us with 38 baskets and the remaining number of points. I think that should get you started!

Answer 2

f = foul shots , d = two pointers , t = three pointers

d = f + 13

f + 2 d + 3 t = 95 ... substituting ... f + 2 f + 26 + 3 t = 95 ... 3 f + 3 t = 69

f + d + t = 53 ... substituting ... f + f + 13 + t = 53 ... 2 f + t = 40

solve the system