Problem 86 - College Algebra Essentials

Question

The price of a dress is reduced by \(40 \% .\) When the dress still does not sell, it is reduced by \(40 \%\) of the reduced price. If the price of the dress after both reductions is \(\$ 72,\) what was the original price?

Step-by-Step Solution

Answer

The original price of the dress was \$200.

Step 1: Define the Problem

In this case, we know the final price of the dress after two consecutive 40% reductions, and it is asked to find out the original price of the dress. Let's consider the original price to be \(x\). Then we can set up the relationship: \(0.6\times (0.6\times x) = 72\).

Step 2: Solve the Equation

First, resolve the brackets in the equation by multiplying 0.6 and 0.6 to get \( 0.36x = 72\). To solve this for \(x\), divide both sides of the equation by 0.36 to get \(x = 72/0.36 \).

Step 3: Calculate Original Price

After simplifying the equation in the previous step, it results in \(x = 200\). This means the original price of the dress was \$200.