Answer:
45 pounds of the chocolate candy and 5 pounds of the peanut butter candy.
Step-by-step 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.
