Question

A merchant wants to mix peanuts worth $3 per pound

with jelly beans worth $1.50 per pound to

make 30 pounds of a mixture worth $2.10

per pound. How many pounds of each

should he use?

Answer 1

This is a system of equations problem:

Part one set up general equations

1) Peanuts = 3x ($3 per pound)

2) Jellybean = 1.5y ($1.50 per pound)

Relate x and y to the information you have

He wants 30lb. total: x + y = 30

He also wants the mixture to be valued at $2.50 per pound = 3x + 1.5y = 30(2.5)

*I'm taking $2.50 times 30 because you want the total cost to equal since he wants $2.50 per pound.

You want to substitute one equation into the other.

x + y = 30

3x + 1.5y = 75

1) x + y = 30 => x = 30 - y

2) 3(30 - y) + 1.5y = 75

3) 90 - 3y + 1.5y = 75

4) -1.5y = -15

5) y = 10lb.

Then plug that into one of the original equations to get x.

6) x+ y = 30 => 10 + x = 30 => x = 20lb.

He wants 20lb. of peanuts and 10lb. of jellybeans