A Sweater Was Marked Up From $ 40 \$40 $40 To $ 50 \$50 $50 . If P P P Is The Percent Increase In The Price Of The Sweater, Which Proportion Can Be Used To Calculate P P P ?A) $\frac{$40 - $50}{$40} =

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Understanding the Problem

When a sweater's price is increased from $40\$40 to $50\$50, it is essential to determine the percent increase in the price. This can be achieved by using a proportion, which is a mathematical statement that two ratios are equal. In this case, the proportion will help us find the percent increase, denoted as pp.

The Formula for Percent Increase

The percent increase in the price of the sweater can be calculated using the following formula:

p=(Increase in PriceOriginal Price)×100p = \left( \frac{\text{Increase in Price}}{\text{Original Price}} \right) \times 100

Creating the Proportion

To create the proportion, we need to identify the increase in price and the original price. The increase in price is the difference between the new price and the original price, which is $50−$40=$10\$50 - \$40 = \$10. The original price is $40\$40.

Writing the Proportion

Using the information above, we can write the proportion as follows:

$10$40=p100\frac{\$10}{\$40} = \frac{p}{100}

Solving for pp

To solve for pp, we can cross-multiply and simplify the equation:

$10$40=p100\frac{\$10}{\$40} = \frac{p}{100}

$10$40×100=p\frac{\$10}{\$40} \times 100 = p

$10×100$40=p\frac{\$10 \times 100}{\$40} = p

$1000$40=p\frac{\$1000}{\$40} = p

p=25p = 25

Conclusion

In conclusion, the proportion $10$40=p100\frac{\$10}{\$40} = \frac{p}{100} can be used to calculate the percent increase in the price of the sweater. By solving for pp, we find that the percent increase is 25%25\%.

Example Use Case

Suppose a store increases the price of a sweater from $40\$40 to $50\$50. Using the proportion above, we can calculate the percent increase in the price:

$10$40=p100\frac{\$10}{\$40} = \frac{p}{100}

p=25%p = 25\%

This means that the price of the sweater has increased by 25%25\%.

Tips and Variations

  • When calculating the percent increase, make sure to use the original price and the increase in price.
  • The proportion can be used to calculate the percent increase in any situation where the original price and the increase in price are known.
  • The percent increase can be expressed as a decimal or a percentage.

Common Mistakes

  • Failing to identify the increase in price and the original price.
  • Not using the correct formula for percent increase.
  • Not solving for pp correctly.

Real-World Applications

  • Calculating the percent increase in the price of a product can help businesses determine the profitability of a product.
  • Understanding the percent increase can help consumers make informed purchasing decisions.
  • The concept of percent increase can be applied to various fields, such as finance, economics, and business.

Final Thoughts

In conclusion, the proportion $10$40=p100\frac{\$10}{\$40} = \frac{p}{100} can be used to calculate the percent increase in the price of a sweater. By understanding the concept of percent increase and using the correct formula, we can make informed decisions in various situations.

Understanding the Problem

When a sweater's price is increased from $40\$40 to $50\$50, it is essential to determine the percent increase in the price. This can be achieved by using a proportion, which is a mathematical statement that two ratios are equal. In this case, the proportion will help us find the percent increase, denoted as pp.

Q&A

Q: What is the percent increase in the price of the sweater?

A: The percent increase in the price of the sweater can be calculated using the proportion $10$40=p100\frac{\$10}{\$40} = \frac{p}{100}.

Q: How do I calculate the percent increase?

A: To calculate the percent increase, you need to identify the increase in price and the original price. The increase in price is the difference between the new price and the original price, which is $50−$40=$10\$50 - \$40 = \$10. The original price is $40\$40. Then, you can use the proportion $10$40=p100\frac{\$10}{\$40} = \frac{p}{100} to solve for pp.

Q: What is the formula for percent increase?

A: The formula for percent increase is:

p=(Increase in PriceOriginal Price)×100p = \left( \frac{\text{Increase in Price}}{\text{Original Price}} \right) \times 100

Q: Can I use the proportion to calculate the percent increase in any situation?

A: Yes, the proportion can be used to calculate the percent increase in any situation where the original price and the increase in price are known.

Q: What is the percent increase in the price of the sweater?

A: Using the proportion $10$40=p100\frac{\$10}{\$40} = \frac{p}{100}, we can solve for pp:

$10$40=p100\frac{\$10}{\$40} = \frac{p}{100}

p=25%p = 25\%

Q: How do I express the percent increase as a decimal?

A: To express the percent increase as a decimal, you can divide the percent increase by 100:

25%=25100=0.2525\% = \frac{25}{100} = 0.25

Q: Can I use the proportion to calculate the percent decrease in the price of the sweater?

A: Yes, you can use the proportion to calculate the percent decrease in the price of the sweater. To do this, you need to identify the decrease in price and the original price. The decrease in price is the difference between the original price and the new price, which is $40−$50=−$10\$40 - \$50 = -\$10. Then, you can use the proportion −$10$40=p100\frac{-\$10}{\$40} = \frac{p}{100} to solve for pp.

Q: What is the percent decrease in the price of the sweater?

A: Using the proportion −$10$40=p100\frac{-\$10}{\$40} = \frac{p}{100}, we can solve for pp:

−$10$40=p100\frac{-\$10}{\$40} = \frac{p}{100}

p=−25%p = -25\%

Conclusion

In conclusion, the proportion $10$40=p100\frac{\$10}{\$40} = \frac{p}{100} can be used to calculate the percent increase in the price of a sweater. By understanding the concept of percent increase and using the correct formula, we can make informed decisions in various situations.

Tips and Variations

  • When calculating the percent increase, make sure to use the original price and the increase in price.
  • The proportion can be used to calculate the percent increase in any situation where the original price and the increase in price are known.
  • The percent increase can be expressed as a decimal or a percentage.

Common Mistakes

  • Failing to identify the increase in price and the original price.
  • Not using the correct formula for percent increase.
  • Not solving for pp correctly.

Real-World Applications

  • Calculating the percent increase in the price of a product can help businesses determine the profitability of a product.
  • Understanding the percent increase can help consumers make informed purchasing decisions.
  • The concept of percent increase can be applied to various fields, such as finance, economics, and business.

Final Thoughts

In conclusion, the proportion $10$40=p100\frac{\$10}{\$40} = \frac{p}{100} can be used to calculate the percent increase in the price of a sweater. By understanding the concept of percent increase and using the correct formula, we can make informed decisions in various situations.