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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of 1-point shots she made
Let b = number of 2-point shots she made
Let c = number of 3-point shots she made
given:
(1) +a+%2B+b+%2B+c+=+356+
(2) +b+=+a+%2B+76+
(3) +a+=+c+%2B+77+
This is 3 equations with 3 unknowns, so it's solvable
(3) +a+=+c+%2B+77+
(3) +c+=+a+-+77+
Substitute (2) and (3) in (1)
(1) +a+%2B+b+%2B+c+=+356+
(1) +a+%2B+a+%2B+76+%2B+a+-+77+=+356+
(1) +3a+-+1+=+356+
(1) +3a+=+357+
+a+=+119+
and
(2) +b+=+a+%2B+76+
(2) +b+=+119+%2B+76+
+b+=+195+
and
(3) +c+=+119+-+77+
+c+=+42+
She made 119 1-point shots
She made 195 2-point shots
She made 42 3-point shots

Answer by mananth(16946) About Me  (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