The Changs updated their bedroom by purchasing a new lamp for $89.95 and a comforter set for $239.99. They paid 2007-03-04-00-00_files/i0120000.jpg% sales tax on their purchases. If the Changs paid $351.72 total, determine if they paid the correct amount.

Question

a.
The Changs family paid $0.33 too much for their purchases.
b.
The Changs family paid $0.99 too much for their purchases.
c.
The Changs family paid $5.94 too much for their purchases.
d.
The Changs family paid the correct amount for their purchases.

Answer 1

To determine if the Changs paid the correct amount, we will first calculate the total cost of their purchases before tax, and then apply the sales tax to see what the total should be.

1. Add the costs of the items:

   • Lamp: $89.95
   • Comforter set: $239.99

   Total cost of items = $89.95 + $239.99 = $329.94

2. Calculate the total amount they paid:

   • Total paid = $351.72

3. Determine the amount paid in sales tax:

   • Sales tax paid = Total paid - Total cost of items
   • Sales tax paid = $351.72 - $329.94 = $21.78

4. Calculate the sales tax rate:

   • Sales tax rate = Sales tax paid / Total cost of items
   • Sales tax rate = $21.78 / $329.94

5. Now, we can calculate the expected total with a known sales tax rate. Assuming a sales tax rate of 6% (for example):

   • Sales tax rate = 0.06 (or 6%)
   • Expected sales tax = Total cost of items * sales tax rate
   • Expected sales tax = $329.94 * 0.06 = $19.7964, rounded to $19.80

6. Calculate the correct total including expected sales tax:

   • Correct total = Total cost of items + Expected sales tax
   • Correct total = $329.94 + $19.80 = $349.74

7. Now, compare the correct total with the total paid:

   • Amount overpaid = Total paid - Correct total
   • Amount overpaid = $351.72 - $349.74 = $1.98

Since we came to the conclusion that they paid $1.98 too much, the options given seem to need reevaluation to fit a scenario that includes this figure, as none match.

However, if we had a different sales tax rate applied initially, it would need to be double-checked to ensure accuracy.

In the case where it's a standard sales tax rate (if for example it was a 7% or 8%), you'd need to verify what exact tax rate is being applied.

Given the answer options provided, it does not precisely match any of those listed. Therefore, it seems there may be a miscalculation in options regarding the rounded amount on the proper calculations.

However, based on the misaligned total after proper math, we suspect that there appears to be a correct series in the amount:

Therefore the most accurate conclusion may lead to a candidate from an assumed tax error on the original terms of basis.

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In this case, if you meant a more fixed sales tax rate like 7%, do let me know! Would be happy to explore that too.