Question

The owner of a grocery store wants to mix two kinds of condy together to make 15lb that he can sell for $5.00 per lb. He wants to use chocolate candies that he sells for $7.00 per lb and sugar candies that he sells for $2.00 per lb. How many pounds of each should the owner use?

Answer 1

9 pounds of chocolate candy

6 pounds of sugar candy

Explanation:

x will represent pounds of chocolate candies used

y will represent pounds of sugar candies used

x + y = 15

x · $7.00 + $2.00 · y = $5.00 · 15

x = 15 - y

(15 - y) · $7.00 + $2.00 · y = $5.00 · 15

105 - $5.00 · y = 75

105 - 75 = $5.00 · y

$30 = $5.00 · y

$30 ÷ $5 = y

$30 ÷ $5 = 6

y = 6

x + y = 15

x + 6 = 15

x + 6 - 6 = 15 - 6

x = 9

Answer 2

Answer: 6 pounds of sugar candy, and 9 pounds of chocolate candy.

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.