Mixtures and Alligation
Weighted average and the alligation rule for mixing two ingredients of different price or strength, plus the repeated-replacement formula for a liquid drawn off and topped up with water.
What you will be able to do
- Compute the price or strength of a mixture as a weighted average of its parts.
- Use the alligation rule to find the ratio in which two ingredients are mixed.
- Apply the repeated-replacement formula for a liquid removed and replaced with water.
- Set up a dilution or concentration change by tracking the amount of the unchanged component.
What is inside this lesson
- 1What a mixture question asks
- 2Weighted average
- 3The alligation rule
- 4Repeated replacement
- 5Dilution and concentration by the unchanged part
- 6Worked example
- 7Common mistakes
- 8Quick revision
- 9Practice
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What a mixture question asks
A mixture question combines two (sometimes more) ingredients that differ in price per unit, or in the fraction of some component such as milk, acid or a metal. It then asks one of: the price or strength of the blend, the ratio the two were mixed in, or how much of one to add to reach a target.
Every one of these is a weighted average in disguise. Alligation is a fast way to run that weighted average backwards to get the ratio.
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