Solving a percent mixture problem using a system of linear equations

Question

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar, and the second brand contains 13% vinegar. The chef wants to make 320 milliliters of a dressing that is 12% vinegar. How much of each brand should she use?

Answer 1

I will set up the system for you and tell you how to solve it, but the arithmetic will be up to you.

F = amt of 5%

T = amt of 13%

F + T = 320

.05F + .13T = .12*320

Multiply the 1st equation by 5 and the second equation by 100.

Subtract so that the F variable is eliminated.

You take it from there.