the harringtons go to a restaurant for lunch and their bill is $86.20. after 6.5% tax and tip, they pay a…

Explanation:

Step1: Calculate the amount of tax

The tax rate is 6.5% of the bill amount. The bill amount is $86.20. So the tax amount $T$ is calculated as $T = 86.20\times0.065$. $T=86.20\times0.065 = 5.603\approx5.60$

Step2: Calculate the total cost of food and tax

Let the cost of food be $B = 86.20$ and tax be $T\approx5.60$. The total cost of food and tax $C_{ft}=B + T$. $C_{ft}=86.20+5.60 = 91.80$

Step3: Calculate the tip amount

The total amount paid is $100$. Let the tip amount be $t$. Then $t=100 - C_{ft}$. $t = 100-91.80=8.20$

Step4: Calculate the tip - percentage

The tip - percentage $p$ is calculated as $p=\frac{t}{B}\times100%$. $p=\frac{8.20}{86.20}\times100%\approx9.51%$

In general, a tip of 15 - 20% is considered a sign of exceptional service. Since the Harringtons' tip percentage is approximately 9.51%, their tip does not reflect that they were exceptionally pleased with the service.

Answer:

No, their tip does not reflect that they were exceptionally pleased with the service because the tip percentage is approximately 9.51%, which is lower than the 15 - 20% range typically associated with exceptional service.