1. **State the problem:** We are given the expression for the total candies in $b$ bags as $$bg + by$$ and asked to find an equivalent expression for the total candies in 1 bag. 2. **Understand the expression:** The expression $$bg + by$$ means $b$ times $g$ plus $b$ times $y$, representing $b$ groups of $g$ green candies and $y$ yellow candies. 3. **Use the distributive property:** The distributive property states that $$a(b + c) = ab + ac$$. Here, we can factor out $b$: $$bg + by = b(g + y)$$ 4. **Interpretation:** The expression $b(g + y)$ means $b$ times the total candies in one bag, where one bag has $g + y$ candies. 5. **Find total candies in 1 bag:** To find the total candies in 1 bag, we remove the factor $b$: $$g + y$$ 6. **Conclusion:** The equivalent expression for the total number of candies in 1 bag is $$g + y$$. **Final answer:** $g + y$