Question

Leah is mixing peanut butter candy (p) that sells for $3.60 per pound with chocolate candy (c) that sells for $2.00 per pound. She needs 50 pounds of the mixture to sell in her store for $2.16 per pound. Which system of linear equations can Leah use to determine the number of pounds of each candy to use?

Answer 1

45 pounds of the chocolate candy and 5 pounds of the peanut butter candy.

Explanation:

let's define the variables:

p = pounds of peanut butter candy she uses

c = pounds of chocolate candy she uses.

We know that she wants to have a total of 50 pounds of the mixture, then we will have that:

p + c = 50

We also want that these 50 pounds sell for $2.16 per pound.

Then we must have that the price for the candies in the mixture must be equal to the desired price, we can write this as:

p*$3.60 + c*$2.00 = (50 )*($2.16 )

Then we have the system of equations:

p + c = 50

p*$3.60 + c*$2.00 = (50)*($2.16) = $108

To solve this, we first need to isolate one of the variables in one of the equations. I will isolate p in the first equation to get:

p = 50 - c

Now we can replace this in the other equation to get:

(50 - c)*$3.60 + c*$2.00 = $108

Now we can solve this for c.

$180 - c*$3.60 + c*$2.00 = $108

$180 - c*$1.60 = $108

$180 - $108 = c*$1.60

$72 = c*$1.60

$72/$1.60 = c = 45

This means that she should use 45 lb of the chocolate candy, and using the equation:

p + c = 50

p + 45 = 50

p = 50 - 45 = 5

p = 5

She should use 5 lb of the peanut butter candy.