At a craft club, Farah and Dmitri had 220 stickers altogether. During the sharing session, Farah gave Dmitri 30 stickers. After the sharing, Farah had 20 more stickers than Dmitri. How many stickers did Farah have before the sharing session?
- 70 stickers
- 100 stickers
- 120 stickers
- 150 stickers
Need a hint?
The 20-sticker gap is after the sharing. Think about what the gap was before 30 stickers changed hands.
Worked answer
- The total number of stickers stays at 220.
- When Farah gives Dmitri 30 stickers, the difference between them shrinks by 2 × 30 = 60.
- So before the sharing, Farah had 20 + 60 = 80 more stickers than Dmitri.
- Let Dmitri have s stickers before the sharing. Farah had s + 80.
- s + (s + 80) = 220
- 2s + 80 = 220, so 2s = 140 and s = 70.
- Farah had 70 + 80 = 150 stickers before the sharing session.
The mistake this question tests
Collecting like terms in algebra
A common mistake is to halve 220 − 20, which gives the number of stickers Dmitri had after the sharing. To find Farah's amount before the sharing, the effect of the 30-sticker giveaway must also be included.
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