Q41. - Algebra 1

Question

SHOPPING A group of girls is shopping for dresses to wear to the spring dance. One finds a dress priced at \(75 with a 20% discount. A second girl finds a dress priced at \)85 with a 30% discount.

a. Find the amount of discount for each dress.

b. Which girl is getting the better price for the dress?

Step-by-Step Solution

Answer

a. Discount on the first dress is $15 and the discount on the second dress is $25.5.

b. The second girl is getting a better deal.

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.

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.

Step 2. Find the discount for the first dress.

We are given that the first girl finds a dress for $75 with a 20% discount and the second girl finds a dress for $85 with a 30% discount.

For the first girl, the discount is 20% of the price. We will subtract this amount from the original price. 

So If x represents the discount then we have:

$\begin{array}{l}\text{x=Discount\%}\times \text{Cost of dress}\\ x=\frac{20}{100}\times 75\\ x=0.20\times 75\\ x=\$15\end{array}$

The discount is $15, also the discounted price of the dress is:

 $\begin{array}{l}\text{Cost of dress}-\text{Discount}\\ =\$75-\$15\\ =\$60\end{array}$ 

Thus, the discounted price of the dress is $60.

Step 3. Find the discount for the second dress.

For the second girl, the discount is 30% of the price. We will subtract this amount from the original price. 

So If y represents the discount then we have:

 $\begin{array}{l}\text{y = Discount\%}\times \text{Cost of dress}\\ y=\frac{30}{100}\times 85\\ y=0.30\times 85\\ y=\$25.5\end{array}$

 The discount is $25.5, also the discounted price of the dress is:

 $\begin{array}{l}\text{Cost of dress}-\text{Discount}\\ =\$85-\$25.5\\ =\$59.5\end{array}$

Thus, the discounted price of the dress is $59.5.

Therefore, the discount on the first dress is $15 and the discount on the second dress is $25.5. And the second girl is getting a better deal.