Percent mixture using system of linear equations

Question

A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12% vinegar. The chef wants to make 160 milliliters of a mixture that contains 23% vinegar. How much vinegar and how much Italian dressing should she use?

vinegar:____

italian dressing:____

Answer 1

Let V = ml of vinegar in mixture

Let D = ml of Italian dressing in mixture

V + D = 160 total volume balance

1.00V + .12D = ..23(160) vinegar balance

I will use substitution and rewrite the first equation as D = 160 - V.

V + .12(160 - V) = .23((160)

V + 19.2 - .12V = 36.8

.88V = 17.6

V = 20

D = 160 - 20 = 140

Now to check (important!)

1.00(20) + .12(140) = 20 + 16.8 = 36.8

Mix 20 ml of vinegar with 140 ml of Italian dressing to make 160 ml of a mixture containing 23% vinegar.