A medium question on percentages and mixtures for P5–P6, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P6 first round and finals: discounts, a rise followed by a fall, and mixtures.
The question
The science lab has two bottles of salt water.
Bottle A holds 400 g at a concentration of 9%; bottle B holds 100 g at 24%.
The teacher pours both into a big beaker and stirs.
What is the concentration of the salt water in the beaker, as a percentage?
Show the hints (2)
💡Hint 1: The bottles weigh different amounts, so you can't just average the two concentrations. Find how many grams of salt each holds.
💡Hint 2: Add up the salt, then see what percentage it is of all the solution.
Worked solution
Have a go first, then read the solution step by step.
1.Bottle A holds 400 × 9 ÷ 100 = 36 g of salt; bottle B holds 100 × 24 ÷ 100 = 24 g.
2.Mixed: salt 36 + 24 = 60 g, solution 400 + 100 = 500 g.
3.Concentration = 60 ÷ 500 × 100% = 12%.
⚠️Common mistake: working out (9 + 24) ÷ 2. Bottle A is heavier, so the mixture ends up closer to its concentration.
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