Q36. - Algebra 1

Question

Find the final price of each item.

Sweater: $14.99  

discount: 12%  

tax: 6.25% 

Step-by-Step Solution

Answer

The final price of the sweater is $14.128.

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. Concept of Discount and sale tax.

Discount is a percentage of the original price that is subtracted from the price of the item the final price is called selling price. It is a percent of the decrease in the cost.

Sales tax is a tax that is added to the price of the item the final price is called selling price. It is a percent of the increase in the cost.

Step 3. Find the new price.

We are given the following price and the discount percentages:

Sweater: $14.99  

discount: 12% 

tax: 6.25%

The discount is 12% of the price. We will subtract this amount from the original price. 

The tax is 6.25% of the price. We will add this amount to the original price. 

So If x represents the new price after subtracting discount then we have:

$\begin{array}{l}x=\text{Cost + }\left(\text{Tax\% of Cost}\right)\text{ - }\left(\text{Discount}\%\text{ of Cost}\right)\\ x=\$14.99+\left(6.25\%\times \$14.99\right)-\left(12\%\times \$14.99\right)\\ x=14.99+\left(\frac{6.25}{100}\times 14.99\right)-\left(\frac{12}{100}\times 14.99\right)\\ x=14.99+\left(0.0625\times 14.99\right)-\left(0.12\times 14.99\right)\\ x=14.99+0.9368-1.7988\\ x=15.9268-1.7988\\ x=\$14.128\end{array}$

Thus, the final price of the sweater is $14.128.