Alright, let's tackle this problem by examining the given data step-by-step for each component of the lunch.
We are comparing the economic costs of a current lunch with a healthier lunch. Here are the costs breakdown:
1. Main course:
- Current lunch: \[tex]$1.15
- Healthier lunch: \$[/tex]1.85
2. Side dish:
- Current lunch: \[tex]$0.30
- Healthier lunch: \$[/tex]0.90
3. Dessert:
- Current lunch: \[tex]$0.30
- Healthier lunch: \$[/tex]0.10
4. Beverage:
- Current lunch: \[tex]$0.30
- Healthier lunch: \$[/tex]0.05
Now, let's determine the price differences for each category:
- Main course:
- Difference: [tex]\(|1.15 - 1.85| = 0.70\)[/tex]
- Side dish:
- Difference: [tex]\(|0.30 - 0.90| = 0.60\)[/tex]
- Dessert:
- Difference: [tex]\(|0.30 - 0.10| = 0.20\)[/tex]
- Beverage:
- Difference: [tex]\(|0.30 - 0.05| = 0.25\)[/tex]
With the price differences calculated, let's summarize them:
- Main course: \[tex]$0.70
- Side dish: \$[/tex]0.60
- Dessert: \[tex]$0.20
- Beverage: \$[/tex]0.25
We see from these calculations that the smallest price difference is \$0.20, which corresponds to the dessert.
So, the smallest price difference between the two lunches is found in the dessert.
