Solving a Percent Increase Word Problem

📝 Practice Worksheets

Percent Increase Practice Writing Percent Increase Expressions Percent Increase - Sales Tax Discounts

🔑 Key Concepts

Percent increase compares how much a value grew to the original value.
The formula is:
\( \text{PI} = \dfrac{\text{New Value} - \text{Original Value}} {\text{Original Value}} \times 100 \)
The original value is the starting amount before the increase happened.
The new value is the final amount after the increase happened.
Always divide by the original value, not the new value.

✏️ Worked Examples — Percent Increase Word Problems

Example 1 — Plant Height

A sunflower was 24 inches tall at the beginning of the month. By the end of the month, it was 30 inches tall. What is the percent increase in height?

First, identify the values.

\( \text{Original Value} = 24 \)

\( \text{New Value} = 30 \)

Use the percent increase formula:

\( \text{PI} = \dfrac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100 \)

Substitute the values into the formula:

\( \dfrac{30 - 24}{24} \times 100 \)

Now subtract to find the increase. This tells us how much the height grew.

\( \dfrac{6}{24} \times 100 \)

Next, divide by the original value.

\( 0.25 \times 100 \)

Finally, convert the decimal to a percent.

\( 25\% \)

Example 2 — Savings Account

Jada had 💲80 in her savings account. After earning money from babysitting, she now has 💲100. What is the percent increase in her savings?

First, identify the values.

\( \text{Original Value} = 80 \)

\( \text{New Value} = 100 \)

Use the percent increase formula:

\( \text{PI} = \dfrac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100 \)

Substitute the values:

\( \dfrac{100 - 80}{80} \times 100 \)

Now subtract to find the amount of increase.

\( \dfrac{20}{80} \times 100 \)

Divide by the original value to see what fraction of the starting amount the increase represents.

\( 0.25 \times 100 \)

Convert to a percent.

\( 25\% \)

Example 3 — Puppy Weight

A puppy weighed 40 pounds at its first checkup. A few months later, it weighed 52 pounds. What is the percent increase in the puppy’s weight?

First, identify the values.

\( \text{Original Value} = 40 \)

\( \text{New Value} = 52 \)

Use the percent increase formula:

\( \text{PI} = \dfrac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100 \)

Substitute the values:

\( \dfrac{52 - 40}{40} \times 100 \)

Subtract first to find the increase in pounds.

\( \dfrac{12}{40} \times 100 \)

Now divide by the original value because percent increase is based on the starting amount.

\( 0.3 \times 100 \)

Convert the decimal to a percent.

\( 30\% \)

💡 Main Idea

To find percent increase, subtract the original value from the new value, divide by the original value, and then multiply by 100. This tells how large the increase is compared to the starting amount.

📚 What You Should Already Know

Before working on percent increase, students should be able to subtract, divide decimals, and convert a decimal to a percent by multiplying by 100.

🚀 What Comes Next

After percent increase, students can move on to percent decrease, discounts, markups, sales tax, and writing expressions that represent percent change situations.

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