🍽️ Mary, Larry, and the plates that cost the same

A closer look at one question · SMC 2026 mock, Question 21 (bank id B6)

Mary had $166 and Larry had $304. Each of them bought 5 of the SAME plates, at the SAME price. Afterwards, Larry had 4 TIMES as much money left as Mary. What was the price of one plate?

1 They spent the SAME amount — so the GAP never changes

Before

Mary $166Larry $304

Gap = 304 − 166 = $138, and it stays $138 after both of them spend the same amount on plates.

2 After: Larry has 4 units, Mary has 1 unit — the gap is 3 units

Mary left

1 unit

Larry left

1u1u1u1u

4 − 1 = 3 units = $138, so 1 unit = $46 — that is Mary's money LEFT.

3 Work out what Mary SPENT on 5 plates

Mary started with $166 and has $46 left, so she spent 166 − 46 = $120 on 5 plates: 120 ÷ 5 = $24 each.

$24

per plate.

The trap: not noticing that the DIFFERENCE stays the same when both people spend the same amount. That one idea turns a hard problem into two divisions.