Proportion Word Problem Solver
Solve everyday "if this much costs/takes that much, how much for…" problems by setting up and cross-multiplying a proportion.
How it works
q1 / r1 = q2 / x → x = r1 ÷ q1 × q2 (cross-multiply)
A proportion states that two ratios are equal, and most rate word problems fit this mould: a known quantity maps to a known result, and you want the result for a new quantity. Cross-multiplying is really just finding the rate per unit (result ÷ known quantity) and multiplying it by the new quantity. Keeping the units consistent on both sides — apples with apples, dollars with dollars — is what makes the setup correct.
Worked example
If 3 apples cost $2.40, the rate is 2.40 ÷ 3 = $0.80 each. For 8 apples the cost is 0.80 × 8 = $6.40 — the same as cross-multiplying 3/2.40 = 8/x.
Frequently asked questions
How do I set up a proportion from a word problem?
Write the known pair as one ratio and the unknown pair as the other, keeping the same quantity on top of both. "3 apples : $2.40" and "8 apples : x" become 3/2.40 = 8/x. Then cross-multiply to solve for x.
What does cross-multiplying do?
It clears the fractions: from 3/2.40 = 8/x you get 3·x = 2.40·8, so x = (2.40·8)/3 = 6.40. It gives the same answer as finding the unit rate and scaling it, just in one step.
Does this only work for prices?
No — any constant-rate relationship works: distance and time at a steady speed, ingredients scaled up in a recipe, or workers and hours on a job. The key assumption is that the ratio stays constant.
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This calculator is for educational purposes. Double-check important results before acting on them.