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.
Mix 8 L of 25% with 4 L of 50% → final %.
- 2.
x L of 10% added to 5 L of 20% to get 15%. Find x.
- 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.
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.
A chemist has 30% and 60% salt solutions. How much of each is needed to make 20 liters of 45% solution?