Math PicnicEvery sheet is a promise

One equation, two unknowns, step by step

Pens are 15c, erasers are 8c, and Mia spent exactly 115c on both.

Practice Practice sheetNew questions
The question

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
  1. Three numbers and two things to find, which normally means it cannot be done. badges are 8c, stickers are 7c, and 83c was spent exactly.
  2. What closes it is that you cannot buy part of one. Whatever is left after the badges has to divide by 7 with nothing over, and that is a test you can run on each number in turn.
  3. 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.
  4. So 6 badges and 5 stickers. The trials that failed are not wasted work — they are the reason this one is the only answer.

How it works.

  1. 01

    Three numbers and two things to find, which normally means it cannot be done. badges are 8c, stickers are 7c, and 83c was spent exactly.

  2. 02

    What closes it is that you cannot buy part of one. Whatever is left after the badges has to divide by 7 with nothing over, and that is a test you can run on each number in turn.

  3. 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.

  4. 04

    So 6 badges and 5 stickers. The trials that failed are not wasted work — they are the reason this one is the only answer.

Pick another skill