Question 5056
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
{{{ (.2y)/.2 = 2.00/.2 = 20/2 }}} 
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