Sam Bought A Special Edition Baseball Card For $ 28 \$28 $28 . When The Player On The Baseball Card Retired, The Value Of The Card Increased. It Is Now Worth 240 % 240\% 240% Of What Sam Paid For The Card. How Much Is The Card Worth Now?

Introduction

In the world of collectibles, rare items can increase in value over time due to various factors such as rarity, demand, and nostalgia. In this article, we will explore a mathematical problem involving a special edition baseball card that has increased in value significantly after the player's retirement. We will use mathematical concepts to determine the current worth of the card.

The Problem

Sam bought a special edition baseball card for $\$28$. When the player on the baseball card retired, the value of the card increased. It is now worth $240\%$ of what Sam paid for the card. We need to find out how much the card is worth now.

Understanding the Concept of Percentage Increase

To solve this problem, we need to understand the concept of percentage increase. A percentage increase is a way to express a change in value as a percentage of the original value. In this case, the value of the card has increased by $240\%$, which means it is now worth $240\%$ of the original value.

Calculating the Percentage Increase

Let's calculate the percentage increase in the value of the card. We know that the original value of the card was $\$28$. The value of the card has increased by $240\%$, which means the new value is $240\%$ of the original value.

To calculate the new value, we can use the following formula:

New Value = Original Value + (Original Value x Percentage Increase)

In this case, the percentage increase is $240\%$, which is equivalent to $2.4$ as a decimal.

New Value = $\$28$+ ($\$28$ x $2.4$)

New Value = $\$28$+ $\$67.20$

New Value = $\$95.20$

Conclusion

The value of the special edition baseball card has increased significantly after the player's retirement. Using the concept of percentage increase, we calculated the new value of the card to be $\$95.20$. This represents a $240\%$ increase in value from the original price of $\$28$.

Real-World Applications

The concept of percentage increase has many real-world applications in finance, economics, and business. It is used to calculate interest rates, investment returns, and price increases. Understanding percentage increase is essential for making informed decisions in these fields.

Example Problems

1. A stock increases in value by $15\%$. If the original value of the stock was $\$100$, what is the new value?
2. A company increases its prices by $20\%$. If the original price was $\$50$, what is the new price?
3. A savings account earns an interest rate of $5\%$. If the original balance was $\$1000$, how much will the account balance be after one year?

Solutions

1. New Value = $\$100$+ ($\$100$ x $0.15$)

New Value = $\$100$+ $\$15$

New Value = $\$115$

2. New Price = $\$50$+ ($\$50$ x $0.20$)

New Price = $\$50$+ $\$10$

New Price = $\$60$

3. Interest Earned = $\$1000$ x $0.05$

Interest Earned = $\$50$

New Balance = $\$1000$+ $\$50$

New Balance = $\$1050$

Conclusion

$$$$$$

Introduction

In our previous article, we explored the concept of percentage increase and its application in calculating the value of a rare baseball card. In this article, we will address some frequently asked questions related to percentage increase and provide detailed explanations to help you understand this concept better.

Q: What is percentage increase?

A: Percentage increase is a way to express a change in value as a percentage of the original value. It is calculated by dividing the change in value by the original value and multiplying by 100.

Q: How do I calculate percentage increase?

A: To calculate percentage increase, you can use the following formula:

Percentage Increase = (Change in Value / Original Value) x 100

For example, if the original value is $\$100$ and the change in value is $\$20$, the percentage increase would be:

Percentage Increase = ($20$ / $\$100$) x 100 = 20%

Q: What is the difference between percentage increase and percentage decrease?

A: Percentage increase and percentage decrease are two different concepts. Percentage increase refers to an increase in value, while percentage decrease refers to a decrease in value. The formula for percentage decrease is the same as for percentage increase, but the change in value is negative.

Q: How do I calculate percentage decrease?

A: To calculate percentage decrease, you can use the following formula:

Percentage Decrease = (Change in Value / Original Value) x 100

For example, if the original value is $\$100$ and the change in value is -$20$, the percentage decrease would be:

Percentage Decrease = (-$20$ / $\$100$) x 100 = -20%

Q: What is the relationship between percentage increase and percentage decrease?

A: Percentage increase and percentage decrease are related in that they are two sides of the same coin. If a value increases by a certain percentage, it means that the value has decreased by the same percentage. For example, if a value increases by 20%, it means that the value has decreased by 20%.

Q: How do I apply percentage increase in real-world scenarios?

A: Percentage increase has many real-world applications in finance, economics, and business. It is used to calculate interest rates, investment returns, and price increases. Understanding percentage increase is essential for making informed decisions in these fields.

Q: What are some common mistakes to avoid when calculating percentage increase?

A: Some common mistakes to avoid when calculating percentage increase include:

• Not considering the original value when calculating percentage increase
• Not using the correct formula for percentage increase
• Not rounding the percentage increase to the correct decimal place
• Not considering the direction of the change in value (increase or decrease)

Conclusion

In conclusion, percentage increase is a fundamental concept in mathematics that has many real-world applications. Understanding percentage increase is essential for making informed decisions in finance, economics, and business. By following the formulas and guidelines outlined in this article, you can calculate percentage increase with confidence and accuracy.

Example Problems

1. A stock increases in value by 15%. If the original value of the stock was $\$100$, what is the new value?
2. A company increases its prices by 20%. If the original price was $\$50$, what is the new price?
3. A savings account earns an interest rate of 5%. If the original balance was $\$1000$, how much will the account balance be after one year?

Solutions

1. New Value = $\$100$+ ($\$100$ x $0.15$)

New Value = $\$100$+ $\$15$

New Value = $\$115$

2. New Price = $\$50$+ ($\$50$ x $0.20$)

New Price = $\$50$+ $\$10$

New Price = $\$60$

3. Interest Earned = $\$1000$ x $0.05$

Interest Earned = $\$50$

New Balance = $\$1000$+ $\$50$

New Balance = $\$1050$