How much cashews at 1.58 per pound must be mixed with walnuts that cost 78 cents per pound to make a mixture of 40 pounds of nuts that cost 1.50 per pound?

Question

How much cashews at 1.58 per pound must be mixed with walnuts that cost 78 cents per pound to make a mixture of 40 pounds of nuts that cost 1.50 per pound?

Answer 1

Let x be the weight of cashews needed.

Since the total weight of the mixture is 40 pounds, the weight of walnuts is 40 - x pounds.

The cost of the mixture is $1.50 per pound, so the cost equation is:

1.58x + 0.78(40-x) = 1.50(40)

1.58x + 31.2 - 0.78x = 60

0.80x = 28.8

x = 36

Therefore, 36 pounds of cashews at $1.58 per pound must be mixed with 4 pounds of walnuts at $0.78 per pound to make a mixture of 40 pounds of nuts that cost $1.50 per pound.