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The Long family spent \[tex]$38.62 for school supplies and \$[/tex]215.78 for new school clothes. They paid \(6 \frac{4}{5} \%\) sales tax on their purchases. If the Long family paid \$269.07 total, determine if they paid the correct amount.

A. The Long family paid \$2.63 too little for their purchases.
B. The Long family paid the correct amount for their purchases.
C. The Long family paid \$1.61 too much for their purchases.
D. The Long family paid \$2.63 too much for their purchases.



Answer :

GinnyAnswer
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.

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