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AlgebraVery hardMixing two salt solutions

Algebra practice question

A chemist mixes a 10 percent salt solution with a 40 percent salt solution to make 300 millilitres of a 30 percent salt solution. How many millilitres of the 40 percent solution are used?

Answer: 200

With a millilitres of the weaker and b of the stronger, a + b = 300 and 0.1a + 0.4b = 90. Substituting a = 300 − b gives 30 + 0.3b = 90, so b = 200.

Common wrong answers

If you answered 100
100 is the amount of the 10 percent solution.
If you answered 150
150 splits the mixture in half.
If you answered 225
225 uses 0.4b = 90 and ignores the weaker solution.

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