Question

In the spring, the owner of a sporting goods store decreases the price of winter gloves from $10.00 to $8.00. She increases the price of swimming goggles from $8.00 to $10.00.Use math to show if the percent of decrease and the percent of increase are the same.

Answer 1

Hello! We can solve this exercise using the Rule of Three:

Spring: $10.00 to $8.00.

Let's consider $10.00 as 100%, and 8 as x%:

$\begin{gathered} \frac{10.00}{8.00}=\frac{100\text{ per cent}}{x\text{ per cent}} \\ \\ \text{multiplying accros:} \\ 10.00\cdot x=8.00\cdot100 \\ 10x=800 \\ x=\frac{800}{10} \\ x=80\text{ per cent} \end{gathered}$

So, to find the percent of decrease we have to subtract the new value from the old value. Look:

100% - 80% = 20% is the percentage of decrease

$8.00 to $10.00.

Now, the other part, solving in a similar way:

$\begin{gathered} \frac{8.00}{10.00}=\frac{100\text{ per cent}}{x\text{ per cent}} \\ \\ 8\cdot x=10\cdot100 \\ 8x=1000 \\ x=\frac{1000}{8} \\ x=125\text{ per cent} \end{gathered}$

125% - 100% = 25% is the percentage of increase

So, 20% of decrease is different from 25% of increase.