A grocer want to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use

The answer to the question

Peanuts: 7 punds

Cashews:3 pounds

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations with the information given:

p + c = 10 pounds

p = 10 - c (first equation)

Where

p = pounds of peanuts

c = pounds of cashews

$4 p + $6.50 c = 10lbs $4.75/lbs (second equation)

Replacing the value of "p"

4 (10-c) + 6.50c = 47.5

40-4c + 6.50c = 47.5

6.50c-4c=47.5-40

2.50c = 7.5

c = 7.5/2.50

c = 3 pounds of cashew s

Replacing "c" in the first equation:

p = 10-c

p = 10-3

p=7 pounds of peanuts