To determine if the Long family paid the correct amount for their purchases, we need to follow these steps:
1. Calculate the total cost before tax:
The cost of school supplies is \( \$38.62 \).
The cost of school clothes is \( \$215.78 \).
So, the total cost before tax is:
[tex]\[
38.62 + 215.78 = 254.40
\][/tex]
2. Determine the sales tax rate:
The sales tax rate given is \( 6 \frac{4}{5} \% \).
Converting this to a decimal, we get:
[tex]\[
6 \frac{4}{5} = 6 + \frac{4}{5} = 6 + 0.8 = 6.8\%
\][/tex]
As a decimal, this is \( 0.068 \).
3. Calculate the sales tax amount:
The sales tax amount is obtained by multiplying the total cost before tax by the sales tax rate:
[tex]\[
254.40 \times 0.068 = 17.2992
\][/tex]
4. Calculate the total cost after adding the tax:
The total cost after tax is:
[tex]\[
254.40 + 17.2992 = 271.6992
\][/tex]
5. Compare the calculated total cost with the amount the Long family actually paid:
The Long family paid \( \$269.07 \).
The difference between what was paid and the total cost after tax is:
[tex]\[
269.07 - 271.6992 = -2.6292
\][/tex]
Since the difference is negative, it means the Long family paid less than the total cost after tax. The absolute value of the difference is:
[tex]\[
| -2.6292 | = 2.6292
\][/tex]
Therefore, the Long family paid \( \$2.63 \) too little for their purchases.
Thus, the correct answer is:
a. The Long family paid [tex]$\$[/tex] 2.63$ too little for their purchases.
