Question

A girl works at a​ delicatessen, and it is her turn to make the zesty olive blend. If arbequina olives are ​$4 per pound and green olives are ​$25 per​ pound, how much of each kind of olive should she mix to get 7 pounds of zesty olive blend that will sell for ​$10 a​ pound?

Answer 1

Let A = the weight of arbequina olives in the mix
Let G = the weight of green olives in the mix

Since we know that the mix is 5 pounds total, we have this:
G + A = 5
G = 5 - A

We are asked for 5 pounds of mix that will sell for $6 per pound, so the total cost is $30.


Therefore, we can form the following equation:

A*9 + G*4 = 30

Using substitution, we can express G in terms of A:

9A + 4*(5-A) = 30
9A + 20 -4A = 30
5A + 20 = 30
5A = 10
A = 2

Therefore A = 2 and G = 3