1. **Problem statement:** Alan and Barry share a box of stickers in the ratio 3:2. Alan gives 20% of his stickers to Clara, who initially has none. We need to find the ratio of Alan's to Barry's to Clara's stickers after this transfer. 2. **Initial distribution:** Let the common multiple be $u$. Then Alan has $3u$ stickers and Barry has $2u$ stickers. 3. **Alan gives 20% of his stickers to Clara:** $$\text{Stickers given by Alan} = 3u \times 20\% = 3u \times \frac{2}{10} = 0.6u$$ 4. **Stickers after transfer:** - Alan: $3u - 0.6u = 2.4u$ - Barry: $2u$ (unchanged) - Clara: $0 + 0.6u = 0.6u$ 5. **Ratio of stickers now:** $$2.4u : 2u : 0.6u$$ 6. **Simplify the ratio by dividing all terms by $0.2u$:** $$\frac{2.4u}{0.2u} : \frac{2u}{0.2u} : \frac{0.6u}{0.2u} = 12 : 10 : 3$$ 7. **Answer for (a):** The ratio of Alan's to Barry's to Clara's stickers is $12 : 10 : 3$. --- 1. **Problem statement (b):** Barry also gives some stickers to Clara. In total, Clara receives 26% of all stickers. Find the fraction of Barry's stickers given to Clara. 2. **Total stickers:** $3u + 2u = 5u$ 3. **Stickers given to Clara in total:** $$26\% \times 5u = 0.26 \times 5u = 1.3u$$ 4. **Stickers Clara already received from Alan:** $0.6u$ 5. **Stickers Clara received from Barry:** $$1.3u - 0.6u = 0.7u$$ 6. **Fraction of Barry's stickers given to Clara:** $$\frac{0.7u}{2u} = \frac{0.7}{2} = 0.35 = \frac{7}{20}$$ 7. **Answer for (b):** The fraction of Barry's stickers given to Clara is $\frac{7}{20}$.