One equation, two unknowns
The question
Badges cost 8c and stickers cost 7c at the school fair. Sam spent all 83c of his money on both.
How many badges, and how many stickers, did he buy?
One total, two unknowns, and only whole things
badges:8·stickers:7· spent:83
left over must divide by7
3×8=24→59
4×8=32→51
5×8=40→43
6×8=48→35
6badgesand5stickers
- Here badges are 8c, stickers are 7c, and 83c was spent exactly.
- Two things to find from one total — but you cannot buy part of one. Whatever is left after the badges has to divide by 7 exactly, so try each number in turn.
- 3 × 8 = 24, leaving 59, which 7 does not go into; 4 × 8 = 32, leaving 51, which 7 does not go into; 5 × 8 = 40, leaving 43, which 7 does not go into; 6 × 8 = 48, leaving 35 — and 35 ÷ 7 = 5, which is whole.
- So 6 badges and 5 stickers.
How it works.
- 01
Here badges are 8c, stickers are 7c, and 83c was spent exactly.
- 02
Two things to find from one total — but you cannot buy part of one. Whatever is left after the badges has to divide by 7 exactly, so try each number in turn.
- 03
3 × 8 = 24, leaving 59, which 7 does not go into; 4 × 8 = 32, leaving 51, which 7 does not go into; 5 × 8 = 40, leaving 43, which 7 does not go into; 6 × 8 = 48, leaving 35 — and 35 ÷ 7 = 5, which is whole.
- 04
So 6 badges and 5 stickers.