Question

The Nut Shack sells hazelnuts for $7.00 per pound and peanuts nuts for $5.30 per pound. How much of each

type should be used to make a 30 pound mixture that sells for $6.43 per pound?

Answer 1

10.06 lbs of peanuts and 19.94 lbs of hazelnuts.

Explanation:

lb=pound

30 lb mixture at $6.43/lb means that the total cost of the mixture is 30×6.43=192.9

Let H = weight of hazelnuts in the mixture.

Let P = weight of the peanuts in the mixture.

Set up a system of equations.

7H + 6.43P = 192.9

H + P = 30

Afterward, input the values into the equations above.

H = 30 - P

7(30-P) + 5.3P = 192.9

210 - 7P + 5.3P = 192.9

210 - 1.7P = 192.9

-1.7P + 210 = 192.9

-1.7P = 192.9 - 210

-1.7P = -17.1

P = -17.1 / -1.7 = 10.06

H = 30 - P = 30 - 10.06 = 19.94

Hence, the mixture contains 10.06 lbs of peanuts and 19.94 lbs of hazelnuts. Hope this helps and have a great day!