Question

A restaurant customer left $1.80 as a tip. The tax was 6% and the tip was 20% of the after tax cost. Which information is not needed to compute the bill after tax and tip? What was the total bill? OA. The customer left a 20% tip. OB. The customer left $1.80 as a tip. C. The tax was 6%. OD. All of this information is needed to solve the Noblem. The total bill is $

Answer 1

The tip is $1.80.

It is 20% of the after tax cost.

The tax is 6%.

We can write the tip amount in function of the bill B as:

$\begin{gathered} \text{Tip}=0.2\cdot(1+0.06)\cdot B=0.2\cdot1.06\cdot B=0.212\cdot B \\ 0.212B=1.80 \\ B=\frac{1.80}{0.212}=8.50 \end{gathered}$

The original bill before tax is $8.50.

If we need to calculate the bill after tax (that is, bill + tax), we don't need to know that the tax is 6%, because we would calculate the bill after tax B' as:

$\begin{gathered} \text{Tip}=0.2\cdot B\text{'}=1.80 \\ B^{\prime}=\frac{1.80}{0.2}=9.00 \end{gathered}$

If we add the tip, the total bill Bt is:

$B_t=B^{\prime}+\text{Tip}=9.00+1.80=10.80$

Answer:

The information that is not needed to calculate the bill after tax is C. the tax was 6%.

The total bill after tax and tip is $10.80.