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. Although, the team made 54 baskets and
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Question 418714: 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. Although, the team made 54 baskets and 15 more 2-pointers than foul shots. How many shots of each kind were made?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of 1-point shots made
Let = number of 2-point shots made
Let = number of 3-point shots made
given:
(1)
(2)
(3)
----------------
This is 3 equations and 3 unknowns, so it's solvable
Multiply both sides of (2) by and
subtract (1) from (2)
(2)
(1)
Substitute from (3)
and
(3)
and
(2)
The number of 1-point shots made were 17
The number of 2-point shots made were 32
The number of 3-point shots made were 5
check:
(1)
(1)
OK
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