Teagan Wolf

2023-03-14

During a clothing store's Bargain Days, the regular price for T-shirts is discounted by $5. There is a state sales tax of 5%, and the$5 discount is applied before the sales tax is calculated. What is the equation that shows the discounted price?

Kiara Rollins

To determine the total cost of the t-shirts, we can use the following formula:
$t=\left(p-d\right)+r\left(p-d\right)$
Where:
t is the total price of the thsirts.
p is the original price of the tshirts.
d is the amount of the discount: \$5 for this problem.
r is the tax rate: 5% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 5% can be written as $\frac{5}{100}$.
We can modify the data we have to provide the following formula:
$t=\left(p-5\right)+\frac{5}{100}\left(p-5\right)$
The right side of the equation can also be written as follows:
$t=1\left(p-5\right)+\frac{5}{100}\left(p-5\right)$
$t=\frac{100}{100}\left(p-5\right)+\frac{5}{100}\left(p-5\right)$
$t=\left(\frac{100}{100}+\frac{5}{100}\right)\left(p-5\right)$
$t=\frac{105}{100}\left(p-5\right)$

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