Q37. - Algebra 1

Question

Find the final price of each item.

Printer: $60.00  

discount: 25%  

tax: 6.75%

Step-by-Step Solution

Answer

Final price of printer is $49.05.

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 increase in the cost.

Step 3. Find the new price.

We are given the following price and the discount percentages:

Printer: $60.00  

discount: 25%   

tax: 6.75% 

The discount is 25% of the price. We will subtract this amount from the original price. 

The tax is 6.75% of the price. We will add this amount to the original price. 

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

$\begin{array}{l}x=\text{Cost + }\left(\text{Tax\% of Cost}\right)\text{ - }\left(\text{Discount}\%\text{ of Cost}\right)\\ x=\$60.00+\left(6.75\%\times \$60.00\right)-\left(25\%\times \$60.00\right)\\ x=60+\left(\frac{6.75}{100}\times 60\right)-\left(\frac{25}{100}\times 60\right)\\ x=60+\left(0.0675\times 60\right)-\left(0.25\times 60\right)\\ x=60+4.05-15\\ x=64.05-15\\ x=\$49.05\end{array}$

Thus, the final price of the printer is $49.05.