Q6. - Algebra 1

Question

Find the total price of each item.

dress: $22.50  

sales tax: 7.5%

Step-by-Step Solution

Answer

The total price of the dress is $24.1875.

Step 1. Use the definition of the percentage change.

The percent change is the increase or decrease in the value of a quantity. If the new value is larger than the original value then it is a percent increase and if the change in value is lesser than the original value it is called percentage decrease.

Step 2. Example of the percentage change.

For example, if a person has 25 dollars and he gets 3 more dollars and now has 28 dollars, its percentage increase is calculated as shown:

$\begin{array}{l}\text{Increase }=28-25=3\\ \%\text{ change = r, then}\\ \frac{3}{25}=\frac{r}{100}\\ r=\frac{3}{25}\times 100\\ =12\%\end{array}$

Sales tax is a percentage of the original cost which is added before selling an item. The final price is called the selling price. 

Step 3. Find the total price change.

If we let the total price of the dress be x, and the original price is $22.50, is given then, x can be calculated as:

 $\begin{array}{l}x=7.5\%\times \$22.50+\$22.50\\ x=\frac{7.5}{100}\times 22.50+22.50\\ x=0.075\times 22.50+22.50\\ x=1.6875+22.50\\ x=\$24.1875\end{array}$

Thus, the total price of the dress is $24.1875.