Find the whole given a part and the percentage

This is new at P6 and it is where percentage questions start to bite, because the whole is no longer printed in the question — it is what you are asked to find. The method is the unitary method: the amount you are given is worth some percentage, so divide by that percentage to get 1%, then multiply by 100. The trap is the reverse-discount question. If a jacket cost $120 after a 20% discount, the usual price is not $120 plus 20% of $120, because the 20% was taken off the bigger, original price. Name the whole first, every time.

Worked example

Problem At a sale, Meiling paid $120 for a jacket after a discount of 20%. What was the usual price of the jacket?

The usual price is the whole here, so the usual price is 100% — the $120 is not.
After a 20% discount she paid 100% − 20% = 80% of the usual price, and that is $120.
Every 20% is worth $120 ÷ 4 = $30, so 100% is $30 × 5 = $150, i.e. $150.
Watch out Adding 20% back to $120 gives $144, not $150. 20% of the sale price is smaller than 20% of the usual price, so it can never undo the discount.
Tip Check backwards: 20% of $150 is $30, and $150 − $30 = $120. Landing exactly on the price paid means the answer is right.
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