Word problems: mixtures, alloys and percents
Set up a before-and-after table for a solution, an alloy and a price, choose x so that the condition holds, and check that the answer suits the story.
- Russia: grade 9
Guide
Mixture, alloy and percent problems are solved with a before-and-after table and one equation. Two of the missions lead to a quadratic equation.
The key rule: the mass of a substance in a mixture is the mass of the mixture times its share, m = p·M, where the share is the percent divided by 100. When mixtures are combined, the masses add and so do the masses of pure substance. The equation says: the new mixture holds as much pure substance as the old ones together.
In the last two problems the equation is quadratic and has two roots. Only one suits the story: you cannot pour 18 l out of a 12 l vessel or cut a price by 190 %. Common slips: taking percents of different amounts, averaging the percents, and answering a different question (the mass of the mixture instead of the water added).