1. ## Mixing Candy

A candy store sells boxes of candy containing caramels and cremes. Each box sells for 12 dollars and 50 cents and holds 30 pieces of candy (all pieces are the same size.) If the caramels cost 25 cents to produce and the cremes cost 45 cents to produce, how many of each should be in a box to make a profit of 3 dollars?

For some reason, I am thinking that two equations in two unknowns applies here.

Let x = number of caramels at 25 cents each

Let y = number of cremes at 45 cents each

There are 30 pieces per box.

My first equation should be
x + y = 30. Yes?

Each box cost 12 dollars and 50 cents.

I think my second equation should be 0.25x + 0.45y = 12.50.

Is any of this correct?

2. ## Re: Mixing Candy

Hmmm...looks like you had one shot of Canadian Club Whisky too many!

To make a 3 dollar profit, production cost of a box must be 9.50 (since it sells for 12.50).

x = number of caramel candies; since a box has 30 candies, then 30-x = creme candies.

.25x + .45(30-x) = 9.50

Clear nuff?

3. ## Re: Mixing Candy

0.25x + 0.45(30 - x) = 9.50

0.25x + 13.5 - 0.45x = 9.50

0.25x - 0.45x = 9.50 - 13.5

-0.2x = -4

x = -4/-0.2

x = 20

In the box, there should be 20 caramels and (30 - 20) or 10 cremes.

Correct?

Yes.

5. ## Re: Mixing Candy

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