A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 5% vinegar. The chef wants to make 150 milliliters of a mixture that contains 24% vinegar. How much vinegar and how much Italian dressing should she use?

Suppose the chef mixes x mL of vinegar with y mL of the dressing with 5% vinegar. She wants to end up with a 150 mL mixture, so

x + y = 150

Each mL of pure vinegar contributes - no surprise here - 1 mL of vinegar to the new mixture. Each mL of the 5% vinegar dressing contributes 0.05 mL of vinegar. She wants a dressing with 24% vinegar, meaning 24% of the 150 mL solution should be vinegar, or 36 mL, so

x + 0.05y = 36

Now

x + y = 150 = => y = 150 - x

x + 0.05 (150 - x) = 36 = => x + 7.5 - 0.05x = 36 = => 0.95x = 28.5 = => x = 30

which gives

y = 150 - x = => y = 120