Question

A grocer wants to mix two kinds of nuts. One kind sells for $2.00 per pound, and the other sells for $2.90 per pound. He wants to mix atotal of 16 pounds and sell it for $2.50 per pound. How many pounds of each kind should he use in the new mix? (Round off the answersto the nearest hundredth.)

Answer 1

Let

x -----> pounds of one kind of nuts ($2.00 per pound)

y ----> pounds of other kind of nuts ($2.90 per pound)

we have that

2x+2.90y=2.50(16) ------> equation 1

x+y=16-----> x=16-y -----> equation 2

solve the system of equations

substitute equation 2 in equation 1

2(16-y)+2.90y=40

solve for y

32-2y+2.90y=40

2.90y-2y=40-32

0.90y=8

y=8.89

Find out the value of x

x=16-8.89

x=7.11

therefore

the answer is

7.11 pounds of one kind of nuts ($2.00 per pound)

8.89 pounds of other kind of nuts ($2.90 per pound)