Leo+DadMade for Leo
Solving Problems Involving Percentages
Rung 4 of 4 · Mastery

Percentages in the Real World

Sales tags, GST on receipts, interest on savings, a tip at the café — and the sneaky reverse question where you're given the sale price and asked the original. This is where it all pays off.


BuildPick a scenario — sale, GST, interest, tip — work out the total, then try the "reverse" challenge.
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Every "real" percentage problem is one of the rung-2 moves in disguise. The skill now is spotting which move, and which number is the whole. Let's tour the four you'll meet most, then the one that trips people up.

Discounts and Sales

A discount is taken off. A $120 jacket at 30% off: the discount is 0.30 × 120 = 36, so you pay 120 − 36 = 84. Quick alternative: 30% off means you pay 70%, so 0.70 × 120 = 84 in one step. Same answer, fewer moves.

GST — the 10% That's Always Added

In Australia, GST is 10% added on top. A part costs $60 before GST: 10% of 60 = 6, so the total is 66. Or in one step, 1.10 × 60 = 66. (Going backwards from a GST-included price is just trap-style reverse work — divide by 1.10.)

Simple Interest and Tips

Simple interest is a percent per year, repeated. $500 at 5% for 3 years: one year earns 0.05 × 500 = 25, so three years earn 25 × 3 = 75. A tip works the same as GST — a percent added to the bill: a 15% tip on a $40 bill is 6, so you pay 46.

The move: spot the percent, spot the whole, then add it on (GST, tip, interest, increase) or take it off (discount). Or jump to the leftover/total percent in one multiply.

Working Backwards — the Reverse Trap

The hardest exam question hides the original. "After 20% off, a jacket is $96 — what was it before?" You can't just add 20% back. Instead: 20% off means you paid 80% of the original, so 96 = 0.80 × original, which means original = 96 ÷ 0.80 = 120. The trick is always the same — figure out what percent the known price represents, then divide to undo it. Flip on the reverse mode in the toy to drill this.

Why This Is the Finish Line

Counting "out of 100" was the "aha". Percent-to-fraction-and-multiply made it quick. Naming the three traps made it safe. But pricing a sale, adding GST, growing your savings and undoing a discount — that's the bit that shows up on receipts, in part-time pay and in the exam. That's mastery.

Us, Thinking Out Loud

Where in our week could we spot a discount, a GST line, or a tip?

The reverse one — why can't we just add the percent back?

Of the four rungs, which should we re-drag in a fortnight?