Unit 2 · Number Theory

1/3 + n×1/6 + 1/6 = 1 — How Many Shops?

Lesson 10 of 15

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Hassan visits several shops. The first takes 1/3 of his pocket money; every other shop takes 1/6. He has 1/6 left. How many shops in total? The trick is setting up one equation: first-shop fraction + (n × each-other-shop fraction) + leftover = 1, then solving for n and adding 1 for the first shop.

Chapters

0:00Introduction
0:21The Question
0:52Standardising the fractions
1:17Tracking the known amounts
1:37Calculating the remaining shops
2:04Final tally & strategic exam tip
2:41Correct answer

Question

Hassan goes to the shops with his pocket money.

He spends 13\frac{1}{3} of it in the first shop, and 16\frac{1}{6} of it in each of the other shops that he visits.

He has 16\frac{1}{6} of his pocket money left at the end.

How many shops does Hassan visit altogether?

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