Question

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chef wants to make 370 milliliters of a dressing that is 11% vinegar. How much of each brand should she use?

Answer 1

Answer: to make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.

You want to setup an equation that will match the word problem. Let's call the amount of the first brand, F and the amount of the second brand, S.

We want the total mixture to be 310mL so: F + S = 310

Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)

Now, we can solve the system of equations using substitution.

F + S = 310

.06F + .11S = .08(310)

F = 310 - S [solve 1st equation for F]

.06(310 - S) + .11S = .08(310) [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

F + 124 = 310 [substitute answer for S back into original equation]

F = 186