SOLUTION: I just can't figure this word problem out. A candy store sells boxes of candy containing carmels and cremes. The box sells for $12.50 and contains 30 pieces of candy. If the car

Question 5056: I just can't figure this word problem out. A candy store sells boxes of candy containing carmels and cremes. The box sells for $12.50 and contains 30 pieces of candy. If the caramels cost .25 to produce and the cremes cost .45 to produce, how many of each should be in each box to make a profit of $3.00? Thank you for your help.. I've been trying for ever.. Thanks Caroline
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Before you start the problem, you need to distinguish between the selling price of the box of candy and teh cost to produce the box of candy. The selling price of the box of candy is $12.50, but then you have to subtract $3.00 profit per box, and the cost to produce the candy is then $9.50 per box.

Let x = number of cremes
y = number of caramels

x+ y = 30
.25x + .45y = 9.50

Multiply the first equation by -.25 in order to make the x terms subtract out:
-.25x - .25y = -.25(30)
.25x + .45y = 9.50

-.25x - .25y = -7.50
.25x + .45y = 9.50

.20y = 2.00 Divide both sides by .2

y = 10 caramels

x+y = 30, substitute y = 10,
x + 10 = 30
x= 20 cremes

Check:
Total cost = $9.50
.25x + .45y = 9.50
.25(20) + .45(10) = 9.50
5.00 + 4.50 = 9.50

R^2 from SCC

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