SOLUTION: A candy store sells boxes of candy containing caramels and cremes.Each box sells for $12.50 and holds 30 pieces of candy (all pieces are the same size).If the caramels cost $0.25 t
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Question 1207745: A candy store sells boxes of candy containing caramels and cremes.Each box sells for $12.50 and holds 30 pieces of candy (all pieces are the same size).If the caramels cost $0.25 to produce and the cremes cost $0.45 to produce,how many of each should be in a box to make a profit of $3? Found 3 solutions by mananth, greenestamps, mccravyedwin:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Let number of caramelsbe x
and number of cremes in the box be y
Candies in each box = 30
x+y=30
The caramels cost $0.25 to produce and the cremes cost $0.45
One box sold for $12.50
Profit goal $3.00
Cost should be $9.50
Cost of candies equation
0.25x+0.45y=9.50
Multiply equation by 4
x+1.80y =38
x+y=30
Subtract the equations
0.80y =8
y=10
x=20
each box should contain:
20 caramels
10 cremes
Here is a solution by an informal method that can be used to solve any 2-part "mixture" problem like this (if formal algebra is not required).
To make a profit of $3 on each box if the selling price is $12.50, the cost of production needs to be $12.50-$3 = $9.50.
The cost of producing 30 caramels would be 30($0.25) = $7.50; the cost of producing 30 cremes would be 30($0.45) = $13.50.
Use mental arithmetic to see that $9.50 is 1/3 of the way from $7.50 to $13.50.
That means 1/3 of the candies should be the more expensive cremes.
This problem is shown to be really comical when you work it the following way!
LOL! J
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.
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. J
Edwin
