Certainly, let's go through this step-by-step.
### Part (a)
1. List of Item Costs:
- Turkey sandwich: \[tex]$5.60
- Chicken salad sandwich: \$[/tex]5.40
- Two coffees: \[tex]$3.40
- Apple pie: \$[/tex]2.85
- Chocolate cake: \[tex]$3.95
2. Round Each Cost to the Nearest Dollar:
- Turkey sandwich ( \$[/tex]5.60 ) rounds to \[tex]$6.
- Chicken salad sandwich ( \$[/tex]5.40 ) rounds to \[tex]$5.
- Two coffees ( \$[/tex]3.40 ) round to \[tex]$3.
- Apple pie ( \$[/tex]2.85 ) rounds to \[tex]$3.
- Chocolate cake ( \$[/tex]3.95 ) rounds to \[tex]$4.
3. Estimated Total for the Rounded Costs:
\[
6 + 5 + 3 + 3 + 4 = 21
\]
### Part (b)
Now let's analyze the given total bill before tax, which is \$[/tex]29.85.
1. Compare Given Bill to the Rounded Total:
- Estimated rounded total: \[tex]$21
- Given bill: \$[/tex]29.85
Since \[tex]$29.85 is significantly higher than \$[/tex]21, we can conclude that the given bill is not reasonable based on our rounded estimate. The rounded total serves as an approximate value; real totals should be relatively close, accounting for possible unrounded decimals, but a significant difference such as \[tex]$8.85 suggests potential discrepancies like additional items, fees, or mistakes.
### Summary:
- Estimated Food Bill (Rounded): \$[/tex]21
- Given Bill: \[tex]$29.85
- Conclusion: The given bill of \$[/tex]29.85 is not reasonable based on our estimated total of \$21.
