Q38. - Algebra 1

Question

Find the final price of each item.

Board game: $25.00  

discount: 15%  

tax: 7.5%

Step-by-Step Solution

Answer

The final price of the board game is $23.125.

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:

Boardgame: $25.00  

discount: 15%    

tax: 7.5%

The discount is 15% of the price. We will subtract this amount from the original price. 

The tax is 7.5% 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:

$\begin{array}{l}x=\text{Cost + }\left(\text{Tax\% of Cost}\right)\text{ - }\left(\text{Discount}\%\text{ of Cost}\right)\\ x=\$25.00+\left(7.5\%\times \$25.00\right)-\left(15\%\times \$25.00\right)\\ x=25+\left(\frac{7.5}{100}\times 25\right)-\left(\frac{15}{100}\times 25\right)\\ x=25+\left(0.075\times 25\right)-\left(0.15\times 25\right)\\ x=25+1.875-3.75\\ x=26.875-3.75\\ x=\$23.125\end{array}$

Thus, the final price of the board game is $23.125.