Mixture and Work Problems

7-7Mixture Problems

Overview

Use a chart: amount × concentration = amount of substance.

Key ideas

  • Rows for each solution and the final mixture.
  • Amounts add; substance amounts add.
  • Solve for the unknown amount or concentration.

Worked examples

Example 1

Problem. Mix 10 L of 30% acid with x L of 60% to get 50% acid. Find x.

Solution. 0.3·10 + 0.6x = 0.5(10 + x) → 3 + 0.6x = 5 + 0.5x → 0.1x = 2 → x = 20.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Mix 8 L of 25% with 4 L of 50% → final %.

  2. 2.

    x L of 10% added to 5 L of 20% to get 15%. Find x.

  3. 3.

    How much pure water added to 8 L of 30% to dilute to 20%?

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    How many liters of a 20% acid solution must be mixed with 10 liters of a 50% acid solution to get a 30% solution?

  2. 2.

    A chemist has 30% and 60% salt solutions. How much of each is needed to make 20 liters of 45% solution?