Problema Solution
A basketball team recently scored a total of 96 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 18 more 2 pointers than foul shots. How many shots of each kind were made?
Answer provided by our tutors
let
x = the number of 2 point field goals
y = the number of 3 point field goals
z = the number of 1 point foul shots
basketball team recently scored a total of 96 points
2x + 3y + z = 96
altogether the team made 53 baskets
x + y + z = 53
18 more 2 pointers than foul shots
x = z + 18
by solving the system of equations
2x + 3y + z = 96
x + y + z = 53
x = z + 18
we find
x = 33 shots
y = 5 shots
z = 15 shots
The number of 1-point shots made were 15.
The number of 2-point shots made were 33.
The number of 3-point shots made were 5.