Question 1207745
<pre>
This problem is shown to be really comical when you work it the following way!
LOL! <font face="wingdings" size=5>J</font>

Suppose each box were to contain 30 caramels and no cremes.

Then the profit would be $12.50 - 30($0.25) = $5.00 per box.

But they would be making too much profit that way! (LOL). They only want to make
$3.00 profit per box.  So they need to swap some of those caramels for cremes to
reduce their profit down to only $3.00 per box instead of $5.00 per box. 

Let x be the number of caramels they need to remove from each box and replace
with x cremes in order to reduce their profit from $5 down to only $3.

Since each creme costs $0.45 and each caramel $0.25, their profit will reduce
by $0.45-$0.25 = $0.20 per swap.

Since they will be making x swaps they will be reducing their total profit by
$0.20x. 

{{{matrix(1,5,

(matrix(9,1,Original, profit, with, 30, caramels,or,"$5",per,box)),

""-"",

(matrix(12,1,loss,of,profit,by,swapping,x,caramels,for,x,cremes, or,"$0.20"*x )),

""="",

(matrix(7,1,Final,lower,desired,profit,of,only,"$3.00")) )}}}

{{{"$5"}}}{{{""-""}}}{{{"$0.20"*x}}}{{{""=""}}}{{{"$3"}}}

{{{5}}}{{{""-""}}}{{{0.20x}}}{{{""=""}}}{{{3}}}

{{{-0.20x}}}{{{""=""}}}{{{3}}}{{{""-""}}}{{{5}}}

{{{-0.20x}}}{{{""=""}}}{{{-2}}}

{{{x}}}{{{""=""}}}{{{(-2)/(-0.20)}}}

{{{x}}}{{{""=""}}}{{{(-2)/(-0.20)}}}

{{{x}}}{{{""=""}}}{{{10}}}

So after 10 swaps, each box will contain 10 cremes and 20 caramels. Then,
they'll have their lower profit of only $3 per box. <font face="wingdings" size=5>J</font>

Edwin</pre>