Question

The owner of a​ health-food store sells dried apples for ​$1.40 per​ quarter-pound, and dried apricots for ​$1.60 per​ quarter-pound. How many pounds of each must he mix together to get 20 lb of a mixture that sells for ​$1.51 per​ quarter-pound?

Answer 1

The owner of the store has to mix 9 lb of dried apples and 11 lb of dried apricots to get 20 lb of the mixture and sell it for $1.51 per​ quarter-pound.

Explanation:

You have that the weight of the apples is x and the weight of the apricots is 20 lb - x.

To know the cost of this mixture you divide the weight by the price:

`(1.40x+1.60(20-x))/(20)=cost`

Since you know that the cost is $1.51, you can solve the equation for x:

`1.40x+1.60*20-1.60x=1.51*20\\1.40x-1.60x=1.51*20-1.60*20\\-0.2x=-1.8\\x=(-1.8)/(-0.2)\\x=9`

Then you have that you need 9 lb of apples and 11 lb of apricots.