Chapter 7.6, Problem 26E

To determine

To justify: Which situation results in a greater final amount.

Answer to Problem 26E

The situation in which, an $80\%$ markup of the wholesale price followed by a $30\%$ discount of the retail price results in a greater final amount.

Explanation of Solution

Given information: An $80\%$ markup of the wholesale price followed by a $30\%$ discount of the retail price, or a $30\%$ markup of the wholesale price followed by an $80\%$ discount of the retail price.

Calculation:

Step1. Here, The markup rate of the wholesale price is $80\%$ , and the discount on the retail price is $30\%$ .

Let, the retail price $=x$

Now, the wholesale price,

  $\begin{array}{l}=x-(x\times 30\%)\\ =x-(x\times \frac{30}{100})\\ =x-0.30x\\ =0.70x\end{array}$

Let’s find the final amount,

  $=$ wholesale price $\times$ ( $100\%+$ markup percent)

  $\begin{array}{l}=0.70x\times (100\%+80\%)\\ =0.70x\times \frac{180}{100}\\ =0.70x\times 1.80\\ =1.26x\end{array}$

Step2. Here, The markup rate of the wholesale price is $30\%$ , and the discount on the retail price is $80\%$ .

Let, the retail price $=x$

Now, the wholesale price,

  $\begin{array}{l}=x-(x\times 80\%)\\ =x-(x\times \frac{80}{100})\\ =x-0.80x\\ =0.20x\end{array}$

Let’s find the final amount,

  $=$ wholesale price $\times$ ( $100\%+$ markup percent)

  $\begin{array}{l}=0.20x\times (100\%+30\%)\\ =0.20x\times \frac{130}{100}\\ =0.20x\times 1.30\\ =0.26x\end{array}$

Hence, The situation in which, an $80\%$ markup of the wholesale price followed by a $30\%$ discount of the retail price results in a greater final amount.