- Salesman interpretation.
The salesman is not right that the price of the printers is reduced by 50%. The salesman is not using percentages correctly because he does not consider that the second reduction was 20% of the reduced price. Percentages are a fraction of the price. The price changes after the first reduction. Therefore, the second reduction should be done at the already reduced price. The salesman makes a mistake by adding up the percentage (20 + 30) making him conclude that the percentage reduction is 50 %.
The calculations would result in a total reduction of 50% of the original price. However, the reduction is 30% for the original price and 20% of the reduced price.
Using manual calculation, if the original price was 2,000 then, the price after the first reduction is (0.7x 2000 = 1400). The price after the second reduction of 20% will be (.8 x 1400= 1120) .Using the salesman’s thought where he concluded that the price reduction after the two price reductions then the price will be (0.5 x 2,000 = 1000). The difference between the two answers is 120. The difference indicates that one of the methods is wrong. There is a huge difference between the final prices of the two methods. Therefore, it is clear that the salesman made a mistake in the conclusion. The salesman uses percentages wrongly by directly adding up the percentages which are related to different prices, which is the original price and the price after the first reduction. The salesman fails to notice that the second percentage reduction was done after the first reduction, and; therefore, the two reductions cannot be both based on the original printer’s price.
- If the salesperson made a mistake in their use of percentage, what mistake did they make? Identify the mistake. Reflect on the salesperson’s thought process, i.e. explain how they got the number 50%.
The salesman made a mistake in the percentages for adding up the percentages of the first price reduction and the percentage of the second reduction. The addition led him to acquire a total percentage reduction of (20 + 30) %= 50%. The salesman thought was that since the percentage reductions were for the same original printer price. The salesman however fails because he fails to identify the fact that the percentages reductions were based on different prices. The second reduction was 20% of the reduced price after the first reduction.
The actual percent reduction from the original price is:
First reduction in price equals to 30% or 0.3 decreases. Equally this can be shown as the client pays 70% of the original price, therefore, the customer gets a reduction of 30%. The second reduction in the price is 20 % of 70% or (0.2 x 0.7) = 1.4. This means that after the second reduction the price in percentages becomes (70-14) % = 56%. The total percentage reduction is 30 + 14) = 44%. The total price reduction in terms of percentages equals (30 + 14) % = 44%. The salesman fails in the analysis of the data provided. He fails to apply thinking correctly since the statement is very clear that the second reduction in price is 20% of the reduced price.
The percentage reduction calculation implies that the direct addition of the percentages is a wrong interpretation. Therefore, the correct method is to take the percentage of the resulting percentage after the first reduction. From the example above with an initial printer price using the percentage formula, the price will be (0.44 X 2000 = 1120). The result concurs with the manual process of price calculation.
