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 8%

vinegar, and the second brand contains 11%

vinegar. The chef wants to make 210

milliliters of a dressing that is 9%

vinegar. How much of each brand should she use?

Answer 1

Let L = vol of 8% and H = vol of 11%

L + H = 210

.08L + .11 H = .09*210

Multiply the 2nd equation by 100 and expand the right side

and

Multiply the 1st equation by 8

8L + 8H = 1680

8L + 11H = 1890

Subtract

3H = 210

You finish it from here!