Questions: Dan paid 498.09 (including sales tax) for a laptop computer. The sales tax in his state is 7%. What was the price of the laptop before the sales tax was added? 463.25 469.75 472.00 465.50

Dan paid 498.09 (including sales tax) for a laptop computer. The sales tax in his state is 7%.

What was the price of the laptop before the sales tax was added?
463.25
469.75
472.00
465.50

Transcript text: Dan paid $\$ 498.09$ (including sales tax) for a laptop computer. The sales tax in his state is $7 \%$. What was the price of the laptop before the sales tax was added? $\$ 463.25$ \$469.75 $\$ 472.00$ $\$ 465.50$

Solution

Solution Steps

Step 1: Convert the sales tax rate from a percentage to a decimal

To convert the sales tax rate $r = 7\%$ to a decimal, we divide by 100: $d = \frac{r}{100} = \frac{7}{100} = 0.07$.

Step 2: Use the relationship between the final price, the original price, and the sales tax rate

The relationship is given by the equation $P_{{final}} = P_{{original}} \times (1 + d)$.

Step 3: Rearrange the equation to solve for the original price

Rearranging the equation gives us $P_{{original}} = \frac{{P_{{final}}}}{{1 + d}}$.

Step 4: Substitute the given values into the equation

Substituting $P_{final} = 498.09$ and $d = 0.07$ into the equation gives us $P_{original} = \frac{498.09}{1 + 0.07} = 465.5$.

Final Answer:

The original price of the item before sales tax was added is $465.5.

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