To determine the smallest price difference between the current lunch and the healthier lunch, let's compare the costs of each component (main course, side dish, dessert, and beverage) from both lunches.
### Given Prices:
- Current Lunch:
- Main Course: \$1.15
- Side Dish: \$0.30
- Dessert: \$0.30
- Beverage: \$0.30
- Healthier Lunch:
- Main Course: \$1.85
- Side Dish: \$0.90
- Dessert: \$0.10
- Beverage: \$0.05
### Finding the Price Differences:
1. Main Course:
[tex]\[
\text{Difference} = \left| 1.85 - 1.15 \right| = \$0.70
\][/tex]
2. Side Dish:
[tex]\[
\text{Difference} = \left| 0.90 - 0.30 \right| = \$0.60
\][/tex]
3. Dessert:
[tex]\[
\text{Difference} = \left| 0.10 - 0.30 \right| = \$0.20
\][/tex]
4. Beverage:
[tex]\[
\text{Difference} = \left| 0.05 - 0.30 \right| = \$0.25
\][/tex]
### Summary of Differences:
- Main Course: \$0.70
- Side Dish: \$0.60
- Dessert: \$0.20
- Beverage: \$0.25
From the calculations above, the smallest price difference between the two lunches is found in the dessert, which has a price difference of \$0.20.
Thus, the correct answer is:
Dessert
