To determine the largest price difference between the current lunch and the healthier lunch across the four components (main course, side dish, dessert, and beverage), let's follow these steps:
1. Calculate the price difference for each component:
- Main course:
[tex]\[
\text{Difference in main course prices} = \$1.85 - \$1.15 = \$0.70
\][/tex]
- Side dish:
[tex]\[
\text{Difference in side dish prices} = \$0.90 - \$0.30 = \$0.60
\][/tex]
- Dessert:
[tex]\[
\text{Difference in dessert prices} = \$0.30 - \$0.10 = \$0.20
\][/tex]
- Beverage:
[tex]\[
\text{Difference in beverage prices} = \$0.30 - \$0.05 = \$0.25
\][/tex]
2. Compare the price differences to find the largest:
- Main course: [tex]\( \$0.70 \)[/tex]
- Side dish: [tex]\( \$0.60 \)[/tex]
- Dessert: [tex]\( \$0.20 \)[/tex]
- Beverage: [tex]\( \$0.25 \)[/tex]
We can see that the largest difference is [tex]\( \$0.70 \)[/tex].
3. Identify the component with the largest difference:
The largest price difference of [tex]\( \$0.70 \)[/tex] is found in the main course.
Therefore, the largest price difference between the two lunches is found in the main course.
