Question

The Nut Barn needs 10 pounds of mixed peanuts and cashews to sell for $8.50 per pound. Cashews alone sell for $10 per pound and peanuts for $7.50 per pound. What is the amount of cashews that can be in the mixture and hold the price to $8.50 per pound?

Answer 1

Mixing peanuts ans cashews

Ans: 4 lbs of cashews, and 6 lbs of peanuts.

Explanation:

Call x the number of pounds of cashews and y the number of pounds of peanuts.
We have x + y = 10 lbs (1).
The x-y mixing costs Nut Barn:
10x + 7.5y = $85. (2)
Solve the 2 equations (1) and (2) to find the 2 unknowns x and y.
(1) --> x = 10 - y. Replace this value of x into (2)
(2) --> 10(10 - y) + 7.5y = 85
100 - 10y + 7.5y = 85.
-2.5y = -15 --> `y = 15/2.5 = 6` lbs--> `x = 10 - 6 = 4` lbs