1. **State the problem:** We need to find the ratio of juniors to adults given two ratios: juniors to children is 1:3, and children to adults is 5:2. 2. **Write down the given ratios:** - Juniors : Children = 1 : 3 - Children : Adults = 5 : 2 3. **Express the ratios with a common term:** We want to relate juniors to adults, so we need to express both ratios with the same middle term (children). 4. **Adjust the ratios to have the same number of children:** - From juniors to children: 1 : 3 - From children to adults: 5 : 2 To combine, make the number of children equal in both ratios. The least common multiple of 3 and 5 is 15. 5. **Scale the ratios:** - Juniors : Children = $1 \times 5 : 3 \times 5 = 5 : 15$ - Children : Adults = $5 \times 3 : 2 \times 3 = 15 : 6$ 6. **Combine the ratios:** Since children are now both 15, the combined ratio is: - Juniors : Children : Adults = 5 : 15 : 6 7. **Find the ratio of juniors to adults:** - Juniors : Adults = 5 : 6 8. **Simplify the ratio:** 5 and 6 have no common factors other than 1, so the ratio is already in simplest form. **Final answer:** The ratio of juniors to adults is $5 : 6$.