Ann Marie wishes to mix peanuts worth $1.38 a pound with cashews worth $2.10 a pound to get 8 pounds of mixture worth $1.65 a pound. How many pounds of peanuts does she need?

5

Explanation:

Let the pound of peanut be represented by x.

Let the pound of cashew be represented by y.

Therefore, x + y = 8

1.38x + 2.1y = 1.65

Since x+y = 8

y = 8-x

Then, 1.38x + 2.1y = 1.65 = 1.38x + 2.1(8 - x) = 1.65 × 8

= 1.38x + 16.8 - 2.1x = 13.2

Collect like terms

1.38x - 2.1x = 13.2 - 16.8

-0.72x = -3.6

x = 3.6/0.72

x = 5

Therefore, Ann needs 5 pounds of peanuts