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Chapter 8: Problem 58

The price of a color printer is reduced by \(30 \%\) of its original price. When it still does not sell, its price is reduced by \(20 \%\) of the reduced price. The salesperson informs you that there has been a total reduction of \(50 \%\). Is the salesperson using percentages properly? If not, what is the actual percent reduction from the original price?

Short Answer

Expert verified
The salesperson is incorrect. The actual total reduction from the original price is 44%, not the claimed 50%.

Step by step solution

01

Understand the problem

Let's assume the original price of the color printer is \$1 (we use 1 for simplicity and easier calculations). It is reduced by 30% of original price, and then further reduced by 20% of the reduced price. We need to compare this with the sales person's claim that there is a total reduction of 50%.
02

Calculate the initial reduction

In the first reduction, the price is reduced by 30%. So, the remaining price becomes \(1 - 0.30 = 0.70\) or 70% of the original.
03

Calculate the second reduction

The second reduction is 20% of the reduced price, i.e., 20% of \$0.70, which is \(0.70 * 0.20 = 0.14\). So, the price after the second reduction is \(0.70 - 0.14 = 0.56\) or 56% of the original.
04

Calculate the actual total reduction

The actual total reduction from the original price is 100% - 56% = 44%.
05

Comparing the reductions

Comparing the actual total reduction with the salesperson's claimed reduction, it's clear that the salesperson is not using percentages properly. The total reduction is 44%, not 50% as claimed.

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Most popular questions from this chapter

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