Percent Change

What does percent change express?

• The total quantity of a given item

• The sum of two different values

• The ratio of a quantity to another

• How much a quantity has increased or decreased compared to its original value

Answer explanation

Percent change is a way to measure how much something has changed from where it began. Imagine you have a toy collection, and you had 10 toys, but now you have 15 toys. The percent change shows you that your collection increased by 50%, which means it's grown a lot compared to how it started. It's a helpful tool to understand how things change over time, like when you want to know how much more money you've saved or how much faster you've become in a race.

A bakery wants to analyze the change in the number of pastries sold from 2010 to 2020. In 2010, they sold 800 pastries. In 2020, the number of pastries sold increased to 1,300. What was the percent increase in the number of pastries sold from 2010 to 2020?

• 62.5%

• 45%

• 35.2%

• 50%

Answer explanation

Step 1: Find the Change

Change = New Value - Old Value

Change = 1,300 pastries - 800 pastries = 500 pastries

Step 2: Calculate the Percent Change

Percent Change = (Change / Original Value) × 100%

Percent Change = (500 / 800) × 100 = 62.5%

So, the number of pastries sold increased by 62.5% from 2010 to 2020, indicating significant growth in the bakery's sales.

A local electronics store is offering a special deal on smartphones. A smartphone that originally cost $400 is now on sale for $320. What is the percent discount on the smartphone?

• 15%

• 20%

• 25%

• 30%

Answer explanation

Step 1: Find the Change

Change = New Value - Old Value

Change = $320 - $400 = -$80 (Note: The negative sign indicates a decrease)

Step 2: Calculate the Percent Change

Percent Change = (Change / Original Value) × 100%

Percent Change = (-80 / 400) × 100 = -20%

Since you're looking for a percent decrease, you'll use the positive value of the percentage change.

Positive percentage change = |-20%| = 20%

So, the smartphone is on sale with a discount rate of 20%, which means customers can save 20% off the original price when purchasing the smartphone during the sale.

Jessica decided to invest in a new company by purchasing 200 shares at $16 per share. After a successful year, the value of each share increased to $18. What is the percent change for the price of each share of stock?

• 8.3%

• 10.2%

• 12.5%

• 15.7%

Answer explanation

Step 1: Find the Change

Change = New Value - Old Value

Change = $18 - $16 = $2

Step 2: Calculate the Percent Change

Percent Change = (Change / Original Value) × 100%

Percent Change = (2 / 16) × 100 = 12.5%

So, the value of each share of stock increased by 12.5% after one year, indicating a positive growth in the investment.

 The mayor of Lakeside Village is interested in the change in the number of households over a decade. In 2010, the village had 5,000 households. In 2020, the number of households decreased to 3,650. What was the percent decrease in the number of households from 2010 to 2020?

• 20%

• 25%

• 30%

• 27%

Answer explanation

Step 1: Find the Change

Change = New Value - Old Value

Change = 3,650 households - 5,000 households = -1,350 households (Note: The negative sign indicates a decrease)

Step 2: Calculate the Percent Change

Percent Change = (Change / Original Value) × 100%

Percent Change = (-1,350 / 5,000) × 100 = -27%

Since you're looking for a percent decrease, you'll use the positive value of the percentage change.

Positive percentage change = |-27%| = 27%

So, the number of households in Lakeside Village decreased by approximately 27% from 2010 to 2020, indicating a decline in the village's population over the decade.