Let's break down the problem step-by-step to determine if the Long family paid the correct amount.
1. Calculate the total cost before tax:
[tex]\[
\text{Total cost before tax} = \text{Cost of school supplies} + \text{Cost of school clothes}
\][/tex]
[tex]\[
\text{Total cost before tax} = \$38.62 + \$215.78 = \$254.40
\][/tex]
2. Convert the sales tax percentage to a decimal:
The sales tax is [tex]\(6 \frac{4}{5} \% \)[/tex].
[tex]\[
6 \frac{4}{5} \% = 6.8\%
\][/tex]
As a decimal, this is:
[tex]\[
\frac{6.8}{100} = 0.068
\][/tex]
3. Calculate the total sales tax:
[tex]\[
\text{Total sales tax} = \text{Total cost before tax} \times \text{Sales tax rate}
\][/tex]
[tex]\[
\text{Total sales tax} = \$254.40 \times 0.068 = \$17.2992
\][/tex]
4. Calculate the total cost including tax:
[tex]\[
\text{Total cost including tax} = \text{Total cost before tax} + \text{Total sales tax}
\][/tex]
[tex]\[
\text{Total cost including tax} = \$254.40 + \$17.2992 = \$271.6992
\][/tex]
For practical purposes, we'll consider this total as approximately \[tex]$271.70 (rounding to the nearest cent).
5. Determine the difference between the amount paid and the total cost including tax:
\[
\text{Difference} = \text{Amount paid} - \text{Total cost including tax}
\]
\[
\text{Difference} = \$[/tex]269.07 - \[tex]$271.70 = -\$[/tex]2.63
\]
The negative sign indicates that the Long family paid \[tex]$2.63 less than the required amount.
6. Select the best answer:
From the choices, the correct option is:
a. The Long family paid \$[/tex]2.63 too little for their purchases.
So, the Long family underpaid by \$2.63, making option A the correct choice.
