Question

A saleswomen sells a dried fruit mixture for $5.7 per pound and nuts for $14.55 per pound. She wants to blend the two to get a 10 pound mixture that she will sell for $9.24 per pound. How much should she use?
to get a 10 pound mixture she should use __ lb of fruit mixture and __ lb of nuts.

Answer 1

Let the fruit mixture of $5.7 per pound be for x pounds.

The nut of $14.55 per pound would then be:   (10 -x).

Since the total blend of both = 10 pounds, selling for $9.24 per pound.

cost of 1st type + cost of second type = Total cost of blend mixture

5.7*x  +    14.55*(10 - x) = 9.24*10

5.7x + 145.5 - 14.55x = 92.4

5.7x - 14.55x = 92.4 - 145.5

-8.85x = -53.1

x =  -53.1/-8.85

x = 6

The other  will be (10 -x) = 10 - 6 = 4.  

She should use 6 lb of fruit mixture and 4 lb of nuts.