Question

The owner of a grocery store wants to mix two types of candy together to make 15 lbs that he he can sell for $5.00 per lb. He wants to use chocolate candy's that he sells for $7:00 a pound and sugar candies that he sells for 2.00 per pound. How many pounds of each should the owner use.

Answer 1

9 pounds of chocolate candies, 6 pounds of sugar candies.

Explanation:

We can set the amount of chocolate candies to x and the amount of sugar candies to 15 - x.

Our equation is:

7x + 2(15 - x) = 5 * 15.

Simplified:

7x + 30 - 2x = 75.

x = 9.

9 pounds of chocolate candies.

15 - 9 = 6.

6 pounds of sugar candies.

Answer 2

9 pounds of chocolate and 6 pounds of sugar candies

Explanation:

Let's define the variables:

C = pounds of chocolate candies used.

S = pounds of sugar candies used.

We know that he wants to make a total of 15lb, then:

C + S = 15

We also want that the price per pound to be equal to 5$.

This means that the price of the 15 pounds will be the same as the price of the un-mixed candies.

C*$7.00 + $2.00*S = $5.00*15

Then we have a system of equations:

C + S = 15

C*$7.00 + $2.00*S = $5.00*15

To solve this system, we need to start by isolating one of the variables, i will isolate C in the first equation:

C = 15 - S

now we can replace that in the other equation:

(15 - S)*$7.00 + $2.00*S = $5.00*15

Now we can solve this for S.

$105 - $5.00*S = $75

$105 - $75 = $5.00*S

$30 = $5.00*S

$30/$5 = S = 6

Then there are 6 pounds of sugar candy, and we can use the equation:

C + S = 15

C + 6 = 15

C = 15 - 6 = 9

There are 9 pounds of chocolate candy in the mix.