Question

A girl works at a​ delicatessen, and it is her turn to make the zesty olive blend. If arbequina olives are ​$9 per pound and green olives are ​$4 per​ pound, how much of each kind of olive should she mix to get 5 pounds of zesty olive blend that will sell for ​$6 a​ pound?

Answer 1

....x the quantity of arbequina olives (in pounds) and y the quantity of green olives (in pounds) to mix to obtain 5 pounds of pungent olive mix.

cost of arbequina olives is $9xdollars, cost of green olives is $4y dollars.

the 5 pound mix must be sold for $6 per pound,

so the total cost must equal 6*5=$30

x+y=5

9x+4y=30

by substitution: x=5-y

replace x :

9(5-y)+4y=30

45-9y+4y=30

-5y=30-45

5y=15

y=3

3 pounds of green olives are needed

calculate x :

x+y=5

x+3=5

x=5-3=2

2 pounds of arbequina olives are needed