To determine which item has the smallest price difference between the current lunch and the healthier lunch, we will evaluate the differences for each item.
Let's list down the prices for each item:
- Main course:
- Current: [tex]$1.15
- Healthier: $[/tex]1.85
- Side dish:
- Current: [tex]$0.30
- Healthier: $[/tex]0.90
- Dessert:
- Current: [tex]$0.30
- Healthier: $[/tex]0.10
- Beverage:
- Current: [tex]$0.30
- Healthier: $[/tex]0.05
Now, let's calculate the price difference for each item:
1. Main course:
[tex]\[
\left| 1.85 - 1.15 \right| = 0.70
\][/tex]
2. Side dish:
[tex]\[
\left| 0.90 - 0.30 \right| = 0.60
\][/tex]
3. Dessert:
[tex]\[
\left| 0.30 - 0.10 \right| = 0.20
\][/tex]
4. Beverage:
[tex]\[
\left| 0.30 - 0.05 \right| = 0.25
\][/tex]
After calculating, we have the price differences for each category:
- Main course: [tex]$0.70
- Side dish: $[/tex]0.60
- Dessert: [tex]$0.20
- Beverage: $[/tex]0.25
The smallest price difference among these is $0.20, which corresponds to the dessert.
Therefore, the smallest price difference between the two lunches is found in the:
[tex]\[
\boxed{\text{dessert}}
\][/tex]
