Algebra - concessions

Question

A basketball concession stand sells a soda for $1.25 , a bag of popcorn for $0.50 , and a candy bar for $1.00 . At one game, 15 fewer candy bars were sold than bags of popcorn. That same night, the number of sodas sold was 11 more than the number of candy bars and bags of popcorn sold altogether. If the concession stand made $132 that night, how many of each item were sold?

Answer 1

1.25*S+.5*P+C = 132

 

P=C+15

 

S=C+P+11

 

Substitute P and S in the the top equation.

 

1.25*(C+P+11)+.5*(C+15)+C = 132

 

Substitute P into the above equation.

 

1.25*(C+(C+15)+11)+.5*(C+15)+C = 132

 

4*C+40=132

 

C=92/4=23

 

If C=23 then P=38

 

If S=C+P+11 then S=38+23+11

 

S=72

 

To "prove" this:

 

1.25*72+.5*38+1*23=132