Finding a Number by Its Percentage

Finding a Number by Its Percentage

If P% of an unknown number X equals a known value A, then: X = A · 100 / P.

Example: Anna spent 900 dollars on a new phone, which was 60% of all the money she had saved. How much money did Anna have originally?

Solution using proportion: Let x be the total amount: 900 — 60%, x — 100%. So x = 900 × 100 / 60 = 1500 dollars.

Simpler rule: To find a number by its percentage, divide the given value by the percentage converted into a fraction: x = 900 ÷ (60/100) = 1500 dollars.

More Examples

A student answered 28 questions correctly, which is 80% of the test. How many questions were on the test? 28 = 0.80 · X, so X = 28 / 0.80 = 35 questions.

After a 20% discount, a jacket costs $76. Original price? The sale price is 80% of the original: 76 = 0.80 · X, so X = 76 / 0.80 = $95.

Useful check: The original number should always be larger than the given value when the percentage is less than 100%.