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Kevin's uncle Dev works in a toy shop as a sales manager. He is responsible for monitoring the number of products sold. The following graph shows the number of toys sold by the shop in one day.

Kids learn and grow through playing with toys that match their developmental stages. Uncle Dev is organizing toys at the shop according to age groups: infants, toddlers, and preschoolers. By category, the circle graph shows the percents of toddler and infant toys and number of preschool toys.

Uncle Dev now wants to examine the percent of changes between visitors over the last two weeks. He prepares the following table that shows the number of people that visited the toy shop.

Solution

a Uncle Dev wants to find the percent of change from the first Monday to the second Monday. Start by recalling the percent of change formula.

Notice that on the first week's Monday $75$ person visited the toy shop but on the second week's Monday $81$ people visited the shop. Since it shows an increase, the amount of change will be found by subtracting the original amount from the new amount.

Note that the new amount is $81$ and the original amount is $75.$

$$\begin{array}{c}\text{Percent of Increase}=\frac{81-75}{75}\end{array}$$

Now calculate this percent of increase!

$\text{Percent of Increase}=\frac{81-75}{75}$

▼

Simplify right-hand side

SubTerms

Subtract terms

$\text{Percent of Increase}=\frac{6}{75}$

ReduceFrac

$\frac{a}{b}=\frac{a/3}{b/3}$

$\text{Percent of Increase}=\frac{2}{25}$

ExpandFrac

$\frac{a}{b}=\frac{a\cdot 4}{b\cdot 4}$

$\text{Percent of Increase}=\frac{8}{100}$

WritePercent

Convert to percent

$\text{Percent of Increase}=8\%$

From the first week to the second week, there exists $8\%$ increase in the number of people that visit the toy shop on Monday.

b This time, the percent of change from Friday to Saturday at the second week needs to be calculated. Start by examining the numbers on those days.

$$\begin{array}{c}\text{Friday}=90\\ \text{Saturday}=75\end{array}$$

Notice that the number of people decreased. This means that the percent of change will be found by using the percent of decrease formula.

Substitute the original amount as $90$ and the new amount as $81$ into the formula.

$$\begin{array}{c}\text{Percent of Decrease}=\frac{90-81}{90}\end{array}$$

Now calculate this percent of decrease!

$\text{Percent of Decrease}=\frac{90-81}{90}$

▼

Simplify right-hand side

SubTerms

Subtract terms

$\text{Percent of Decrease}=\frac{9}{90}$

ReduceFrac

$\frac{a}{b}=\frac{a/9}{b/9}$

$\text{Percent of Decrease}=\frac{1}{10}$

ExpandFrac

$\frac{a}{b}=\frac{a\cdot 10}{b\cdot 10}$

$\text{Percent of Decrease}=\frac{10}{100}$

WritePercent

Convert to percent

$\text{Percent of Decrease}=10\%$

The number of people that visit the toys shop is $10\%$ decreased from Friday to Saturday in the second week.

A customer falls in love with a toy for her daughter. It is called Luchador Teddy! Wait. It is missing a price. Uncle Dev estimates that it costs $\$12$ and writes that. The customer goes to the register to buy it but sees she is about to be charged $\$13.50!$

This lesson introduced how to find the percent of change using original and new amounts. The challenge presented at this chapter's start focuses on Kevin's tough decision. If he accepts the loan, he could get his dream bicycle. On the other hand, he could owe too large of an amount!

Extra

Kevin Makes a Counteroffer

The two regather after Kevin found the percent change that his Uncle originally offered.

Uncle Dev is impressed, and embarrassed, by Kevin's math skills. Uncle Dev agrees to the counteroffer — realizing the overpayment.

The two can now take a cruise around town together!