SOLUTION: boxes of candy are sold for $12.50 and holds 30 pieces of candy, some creme and others carmel. Carmel cost $0.25 and creams cost $0.45 how many should be made of each to make a $3

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: boxes of candy are sold for $12.50 and holds 30 pieces of candy, some creme and others carmel. Carmel cost $0.25 and creams cost $0.45 how many should be made of each to make a $3       Log On


   

Question 845360: boxes of candy are sold for $12.50 and holds 30 pieces of candy, some creme and others carmel. Carmel cost $0.25 and creams cost $0.45 how many should be made of each to make a $3 profit
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
One would figure that the 3 dollar profit comes from the selling price, so the non-profit part of the selling price is $9.50.

x for count of creme pieces
y for count of carmel pieces

Accounting for price: 0.45x%2B0.25y=9.50
Accounting for total pieces per box: x%2By=30

This is a system of two linear equations with two unknowns.
Multiply the price equation by 20.
9x%2B5y=190.

SOLVE THE SYSTEM:
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x+y=30
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9x+5y=190
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Elimination Method, factor of 5 upon the piece count equation,
9x%2B5y-%285x%2B5y%29=190-150
4x=40
highlight%28x=10%29 and from this, highlight%28y=20%29.
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ANSWER: 10 creme pieces and 20 carmel pieces.