SOLUTION: In a recent season, Monique Currie of the Duke Blue Devils scored 635 points. She made a total of 356 shots, including 3 point field goals, 2-point field goals, and 1-point free th

Question 445878: In a recent season, Monique Currie of the Duke Blue Devils scored 635 points. She made a total of 356 shots, including 3 point field goals, 2-point field goals, and 1-point free throws. She made 76 more 2-point field goals than free throws and 77 more free throws than 3-point field goals. Find the number of each type of shot she made.
Appreciate if someone can help.

Found 2 solutions by josmiceli, mananth:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of 1-point shots she made
Let = number of 2-point shots she made
Let = number of 3-point shots she made
given:
(1)
(2)
(3)
This is 3 equations with 3 unknowns, so it's solvable
(3)
(3)
Substitute (2) and (3) in (1)
(1)
(1)
(1)
(1)

and
(2)
(2)

and
(3)

She made 119 1-point shots
She made 195 2-point shots
She made 42 3-point shots
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Free throw goals =x
2pt field goals = x+76
3pt field goals=x-77
x+x+76+x-77=356
3x-1=356
3x=357
x=119 free throw goals
x+76 = 2 pt field goals = 119 +76=195
x-77 = 119-77 = 42 -- 3pt goals
CHECK
119*1 + 2*195+3*42= 635 points

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