Solve a percent mixture

Question

A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 8% vinegar. The chef wants to make 60 milliliters of a mixture that contains 31% vinegar. How much vinegar and how much Italian dressing should she use?

Answer 1

.08(60-x) + (1)x = (.31)(60)

x-.08x = 18.6 -4.8

.92x = 13.8

x = 13.8/.92 = 15 mL of pure vinegar mixed with 45 mL 8% vinegar yields 60 mL of 31% vinegar dressing

8 is within 23 of 31

100 is within 69 of 31

69/23 = 3

(60-15)/15 = 45/15 = 3

the chef needs 3 times as much 8% as pure vinegar. 45 is 3 times 15 mL

the chef needs 3 times as much of the solution that is 3 times closer to the mixture's percent of vinegar