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?

Question

Brittany

Mathematics

23 June, 02:05

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?

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Rambo · 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