Question

You wish to make a snack mixes from peanuts and almonds to sell in your health-food store. Mix A is half peanuts and half almonds. Mix B is one fourth peanuts and three-fourths almonds. If you have 15 pounds of peanuts and 20 pounds of almonds, how many pounds of each mix should you make to exactly use all of your ingredients?

Answer 1

25 pounds of mix A

10 pounds of mix B

Explanation:

Each pound of mix A takes half a pound of peanuts and each pound of mix B takes one fourth of a pound of peanuts. Total peanuts consumption is:

`0.5A+0.25B=15`

Each pound of mix A takes half a pound of almonds and each pound of mix B takes three fourths of a pound of almonds. Total almonds consumption is:

`0.5A+0.75B=20`

Solving the linear system:

`0.5A+0.25B=15\\0.5A+0.75B=20\\0.5B=5\\B=10\ pounds\\0.5A=15-0.25*10\\A=25\ pounds`

In order to exactly use all of your ingredients, you should make 25 pounds of mix A and 10 pounds of mix B