Question

The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent. Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent. Explain how a calculation for change in percentage (increase or decrease) is different from a calculation that involves multiplying by percentages. Why is the wording of percentage problems so important? Give examples to illustrate your point.

Answer 1

Explanation:

Given the expressions :

The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent.

Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent.

Let the original price = x

Expression 1 : The list price of the item is 80 percent of the original price

List price = 80% of x

List price = 0.8x

Expression 2: The price of the item has been reduced by 80 percent

Price = x - 80% of x

Price = x - 0.8x

Price = 0.2x

Multiply by percentages is different from an Incremental or decrement in percentage. The first expression above signifies a direct multiplication by the stated percentage while the second signifies a decrease in price based on a certain percentage of the original price.

Wording of percentages are so important for clarity in other to understand if the statement signifies a direct application of the percentage prescribed or a change in quantity, amount or size relative to the base unit.