Question: Lorenzo and his sister, Mariana, are decorating gingerbread houses. They want to make grass, so they turn their icing green by mixing yellow and blue food coloring. Both of them use the same amount of yellow food coloring, but Mariana adds less blue food coloring than Lorenzo. Whose icing is a darker shade of green?
1. **State the problem:** Lorenzo and Mariana mix yellow and blue food coloring to make green icing. Both use the same amount of yellow, but Mariana uses less blue than Lorenzo. We need to determine whose icing is a darker shade of green.
2. **Understanding the color mixing:** The shade of green depends on the ratio of blue to yellow food coloring. More blue relative to yellow results in a darker green.
3. **Set variables:** Let the amount of yellow food coloring be $Y$ for both.
Let Lorenzo's blue amount be $B_L$ and Mariana's blue amount be $B_M$.
Given $B_M < B_L$ and $Y$ is the same for both.
4. **Compare ratios:** Lorenzo's blue-to-yellow ratio is $\frac{B_L}{Y}$.
Mariana's blue-to-yellow ratio is $\frac{B_M}{Y}$.
Since $B_M < B_L$ and $Y$ is the same, we have:
$$\frac{B_M}{Y} < \frac{B_L}{Y}$$
5. **Interpretation:** Lorenzo has a higher blue-to-yellow ratio, so his icing has more blue relative to yellow.
6. **Conclusion:** Lorenzo's icing is a darker shade of green because it contains more blue food coloring relative to yellow.
**Final answer:** Lorenzo's icing is a darker shade of green.