Understanding Percent Problems

Oct 13, 2025 by miodeya.com 23 views

Understanding Percent Problems

Percent problems are a type of mathematical problem that involves finding a percentage of a given number. In this article, we will explore how to solve percent problems, including finding the total price of an item including sales tax.

A Real-World Example

Gina is shopping for a new bicycle. The price of the bicycle is $\$ 300$ and there is an $8 \%$ sales tax. Gina wants to know the total price of the bicycle including sales tax.

Step 1: Identify the Problem

The problem is to find the total price of the bicycle including sales tax. We are given the price of the bicycle ( $\$ 300$ ) and the sales tax rate ( $8 \%$ ).

Step 2: Convert the Sales Tax Rate to a Decimal

To find the sales tax amount, we need to convert the sales tax rate from a percentage to a decimal. To do this, we divide the sales tax rate by 100.

$8 \% = \frac{8}{100} = 0.08$

Step 3: Find the Sales Tax Amount

Now that we have the sales tax rate as a decimal, we can find the sales tax amount by multiplying the price of the bicycle by the sales tax rate.

Sales tax amount = Price of bicycle x Sales tax rate = $\$ 300$ x 0.08 = $\$ 24$

Step 4: Find the Total Price

Finally, we can find the total price of the bicycle including sales tax by adding the sales tax amount to the price of the bicycle.

Total price = Price of bicycle + Sales tax amount = $\$ 300$ + $\$ 24$ = $\$ 324$

Conclusion

In this article, we learned how to solve percent problems, including finding the total price of an item including sales tax. We used a real-world example to illustrate the steps involved in solving a percent problem. By following these steps, you can easily solve percent problems and find the total price of an item including sales tax.

Practice Quiz

Try solving the following percent problem:

A shirt is on sale for $\$ 20$ off its original price of $\$ 50$ . What is the sale price of the shirt?

Step 1: Identify the Problem

The problem is to find the sale price of the shirt. We are given the original price of the shirt ( $\$ 50$ ) and the discount amount ( $\$ 20$ ).

Step 2: Find the Discount Amount

To find the sale price, we need to subtract the discount amount from the original price.

Discount amount = Original price - Discount amount = $\$ 50$ - $\$ 20$ = $\$ 30$

Step 3: Find the Sale Price

Finally, we can find the sale price by subtracting the discount amount from the original price.

Sale price = Original price - Discount amount = $\$ 50$ - $\$ 30$ = $\$ 20$

Answer

The sale price of the shirt is $\$ 20$ .

Solving Percent Problems with Percents

In this section, we will explore how to solve percent problems using percents.

A Real-World Example

A store is offering a $15 \%$ discount on all items. If a shirt originally costs $\$ 40$ , how much will you pay for the shirt after the discount?

Step 1: Identify the Problem

The problem is to find the price of the shirt after the discount. We are given the original price of the shirt ( $\$ 40$ ) and the discount rate ( $15 \%$ ).

Step 2: Convert the Discount Rate to a Decimal

To find the discount amount, we need to convert the discount rate from a percentage to a decimal. To do this, we divide the discount rate by 100.

$15 \% = \frac{15}{100} = 0.15$

Step 3: Find the Discount Amount

Now that we have the discount rate as a decimal, we can find the discount amount by multiplying the original price of the shirt by the discount rate.

Discount amount = Original price x Discount rate = $\$ 40$ x 0.15 = $\$ 6$

Step 4: Find the Sale Price

Finally, we can find the sale price by subtracting the discount amount from the original price.

Sale price = Original price - Discount amount = $\$ 40$ - $\$ 6$ = $\$ 34$

Conclusion

In this article, we learned how to solve percent problems using percents. We used a real-world example to illustrate the steps involved in solving a percent problem. By following these steps, you can easily solve percent problems and find the price of an item after a discount.

Practice Quiz

Try solving the following percent problem:

A store is offering a $20 \%$ discount on all items. If a pair of shoes originally costs $\$ 60$ , how much will you pay for the shoes after the discount?

Step 1: Identify the Problem

The problem is to find the price of the shoes after the discount. We are given the original price of the shoes ( $\$ 60$ ) and the discount rate ( $20 \%$ ).

Step 2: Convert the Discount Rate to a Decimal

To find the discount amount, we need to convert the discount rate from a percentage to a decimal. To do this, we divide the discount rate by 100.

$20 \% = \frac{20}{100} = 0.20$

Step 3: Find the Discount Amount

Now that we have the discount rate as a decimal, we can find the discount amount by multiplying the original price of the shoes by the discount rate.

Discount amount = Original price x Discount rate = $\$ 60$ x 0.20 = $\$ 12$

Step 4: Find the Sale Price

Finally, we can find the sale price by subtracting the discount amount from the original price.

Sale price = Original price - Discount amount = $\$ 60$ - $\$ 12$ = $\$ 48$

Answer

The sale price of the shoes is $\$ 48$ .

Solving Percent Problems with Percent Increase

In this section, we will explore how to solve percent problems using percent increase.

A Real-World Example

A store is offering a $25 \%$ increase on all items. If a shirt originally costs $\$ 30$ , how much will you pay for the shirt after the increase?

Step 1: Identify the Problem

The problem is to find the price of the shirt after the increase. We are given the original price of the shirt ( $\$ 30$ ) and the increase rate ( $25 \%$ ).

Step 2: Convert the Increase Rate to a Decimal

To find the increase amount, we need to convert the increase rate from a percentage to a decimal. To do this, we divide the increase rate by 100.

$25 \% = \frac{25}{100} = 0.25$

Step 3: Find the Increase Amount

Now that we have the increase rate as a decimal, we can find the increase amount by multiplying the original price of the shirt by the increase rate.

Increase amount = Original price x Increase rate = $\$ 30$ x 0.25 = $\$ 7.50$

Step 4: Find the New Price

Finally, we can find the new price by adding the increase amount to the original price.

New price = Original price + Increase amount = $\$ 30$ + $\$ 7.50$ = $\$ 37.50$

Conclusion

In this article, we learned how to solve percent problems using percent increase. We used a real-world example to illustrate the steps involved in solving a percent problem. By following these steps, you can easily solve percent problems and find the price of an item after an increase.

Practice Quiz

Try solving the following percent problem:

A store is offering a $30 \%$ increase on all items. If a pair of shoes originally costs $\$ 40$ , how much will you pay for the shoes after the increase?

Step 1: Identify the Problem

The problem is to find the price of the shoes after the increase. We are given the original price of the shoes ( $\$ 40$ ) and the increase rate ( $30 \%$ ).

Step 2: Convert the Increase Rate to a Decimal

To find the increase amount, we need to convert the increase rate from a percentage to a decimal. To do this, we divide the increase rate by 100.

$30 \% = \frac{30}{100} = 0.30$

Step 3: Find the Increase Amount

Now that we have the increase rate as a decimal, we can find the increase amount by multiplying the original price of the shoes by the increase rate.

Increase amount = Original price x Increase rate = $\$ 40$ x 0.30 = $\$ 12$

Step 4: Find the New Price

Finally, we can find the new price by adding the increase amount to the original price.

New price = Original price + Increase amount = $\$ 40$ + $\$ 12$ = $\$ 52$

Answer

The new price of the shoes is $\$ 52$ .

Solving Percent Problems with Percent Decrease

In this section, we will explore how to solve percent problems using percent decrease.

A Real-World Example

$A store is offering a $20 \%$ decrease on all items. If a shirt originally costs<br/> **Solve Percent Problems, Part 2 - Q&A**$

Frequently Asked Questions

In this article, we will answer some frequently asked questions about solving percent problems.

Q: What is a percent problem?

A: A percent problem is a type of mathematical problem that involves finding a percentage of a given number.

Q: How do I solve a percent problem?

A: To solve a percent problem, you need to follow these steps:

Identify the problem: Read the problem carefully and identify what you are asked to find.
Convert the percent to a decimal: Convert the percent to a decimal by dividing it by 100.
Find the amount: Multiply the number by the decimal to find the amount.
Add or subtract: Add or subtract the amount from the original number to find the final answer.

Q: What is the difference between a percent increase and a percent decrease?

A: A percent increase is when the price of an item goes up by a certain percentage, while a percent decrease is when the price of an item goes down by a certain percentage.

Q: How do I find the sale price of an item after a discount?

A: To find the sale price of an item after a discount, you need to subtract the discount amount from the original price.

Q: How do I find the price of an item after an increase?

A: To find the price of an item after an increase, you need to add the increase amount to the original price.

Q: What is the formula for finding the sale price of an item after a discount?

A: The formula for finding the sale price of an item after a discount is:

Sale price = Original price - Discount amount

Q: What is the formula for finding the price of an item after an increase?

A: The formula for finding the price of an item after an increase is:

New price = Original price + Increase amount

Q: How do I convert a percent to a decimal?

A: To convert a percent to a decimal, you need to divide it by 100.

Q: What is the difference between a percent and a decimal?

A: A percent is a way of expressing a value as a fraction of 100, while a decimal is a way of expressing a value as a fraction of 10.

Q: How do I find the amount of a discount or an increase?

A: To find the amount of a discount or an increase, you need to multiply the original price by the decimal.

Q: What is the formula for finding the amount of a discount or an increase?

A: The formula for finding the amount of a discount or an increase is:

Amount = Original price x Decimal

Q: How do I find the total price of an item including sales tax?

A: To find the total price of an item including sales tax, you need to add the sales tax amount to the original price.

Q: What is the formula for finding the total price of an item including sales tax?

A: The formula for finding the total price of an item including sales tax is:

Total price = Original price + Sales tax amount

Conclusion

In this article, we answered some frequently asked questions about solving percent problems. We hope that this article has helped you to understand how to solve percent problems and find the sale price of an item after a discount, the price of an item after an increase, and the total price of an item including sales tax.

Practice Quiz

Try solving the following percent problem:

A shirt is on sale for $\$ 20$ off its original price of $\$ 50$ . What is the sale price of the shirt?

Step 1: Identify the Problem

The problem is to find the sale price of the shirt. We are given the original price of the shirt ( $\$ 50$ ) and the discount amount ( $\$ 20$ ).

Step 2: Find the Discount Amount

To find the sale price, we need to subtract the discount amount from the original price.

Discount amount = Original price - Discount amount = $\$ 50$ - $\$ 20$ = $\$ 30$

Step 3: Find the Sale Price

Finally, we can find the sale price by subtracting the discount amount from the original price.

Sale price = Original price - Discount amount = $\$ 50$ - $\$ 30$ = $\$ 20$

Answer

The sale price of the shirt is $\$ 20$ .

Solving Percent Problems with Word Problems

In this section, we will explore how to solve percent problems using word problems.

A Real-World Example

A store is offering a $25 \%$ discount on all items. If a shirt originally costs $\$ 40$ , how much will you pay for the shirt after the discount?

Step 1: Identify the Problem

The problem is to find the price of the shirt after the discount. We are given the original price of the shirt ( $\$ 40$ ) and the discount rate ( $25 \%$ ).

Step 2: Convert the Discount Rate to a Decimal

To find the discount amount, we need to convert the discount rate from a percentage to a decimal. To do this, we divide the discount rate by 100.

$25 \% = \frac{25}{100} = 0.25$

Step 3: Find the Discount Amount

Now that we have the discount rate as a decimal, we can find the discount amount by multiplying the original price of the shirt by the discount rate.

Discount amount = Original price x Discount rate = $\$ 40$ x 0.25 = $\$ 10$

Step 4: Find the Sale Price

Finally, we can find the sale price by subtracting the discount amount from the original price.

Sale price = Original price - Discount amount = $\$ 40$ - $\$ 10$ = $\$ 30$

Conclusion

In this article, we learned how to solve percent problems using word problems. We used a real-world example to illustrate the steps involved in solving a percent problem. By following these steps, you can easily solve percent problems and find the price of an item after a discount.

Practice Quiz

Try solving the following percent problem:

A store is offering a $30 \%$ discount on all items. If a pair of shoes originally costs $\$ 60$ , how much will you pay for the shoes after the discount?

Step 1: Identify the Problem

The problem is to find the price of the shoes after the discount. We are given the original price of the shoes ( $\$ 60$ ) and the discount rate ( $30 \%$ ).

Step 2: Convert the Discount Rate to a Decimal

To find the discount amount, we need to convert the discount rate from a percentage to a decimal. To do this, we divide the discount rate by 100.

$30 \% = \frac{30}{100} = 0.30$

Step 3: Find the Discount Amount

Now that we have the discount rate as a decimal, we can find the discount amount by multiplying the original price of the shoes by the discount rate.

Discount amount = Original price x Discount rate = $\$ 60$ x 0.30 = $\$ 18$

Step 4: Find the Sale Price

Finally, we can find the sale price by subtracting the discount amount from the original price.

Sale price = Original price - Discount amount = $\$ 60$ - $\$ 18$ = $\$ 42$

Answer

The sale price of the shoes is $\$ 42$ .