1. **State the problem:** We are given the expression for the total number of candies in $b$ bags as $$bg + by$$ where $g$ is the number of green candies per bag and $y$ is the number of yellow candies per bag. 2. **Goal:** Find an equivalent expression that shows the total number of candies in just 1 bag. 3. **Formula and rules:** The expression $$bg + by$$ can be factored by taking $b$ as a common factor: $$bg + by = b(g + y)$$ This means the total candies in $b$ bags is $b$ times the total candies in 1 bag. 4. **Find total candies in 1 bag:** To find the total candies in 1 bag, divide the total candies in $b$ bags by $b$: $$\frac{bg + by}{b} = \frac{b(g + y)}{b}$$ 5. **Cancel common factor $b$:** $$= \cancel{b}(g + y)/\cancel{b} = g + y$$ 6. **Interpretation:** The total number of candies in 1 bag is the sum of green and yellow candies in that bag, which is $$g + y$$. **Final answer:** $$g + y$$