Calculating the Number of Pennies

Oct 13, 2025 by magicalceylontours.com 131 views

Eric has a vast collection of coins, consisting of pennies, nickels, and quarters. To determine the number of quarters in his collection, we need to first calculate the number of pennies and nickels, and then subtract the total number of these coins from the total number of coins in the collection.

Calculating the Number of Pennies

We are given that ${$ \frac{11}{20}$}$ of the coins in Eric's collection are pennies. To find the number of pennies, we can multiply the total number of coins by this fraction.

Number of pennies = Total number of coins \* \frac{11}{20}

Given that Eric has 240 coins in his collection, we can substitute this value into the equation:

Number of pennies = 240 \* \frac{11}{20}

To simplify this expression, we can multiply the numerator (11) by 240 and then divide by the denominator (20):

Number of pennies = \frac{11 \* 240}{20}

Number of pennies = \frac{2640}{20}

Number of pennies = 132

So, Eric has 132 pennies in his collection.

Calculating the Number of Nickels

We are given that ${$ \frac{4}{20}$}$ of the coins in Eric's collection are nickels. To find the number of nickels, we can multiply the total number of coins by this fraction.

Number of nickels = Total number of coins \* \frac{4}{20}

Given that Eric has 240 coins in his collection, we can substitute this value into the equation:

Number of nickels = 240 \* \frac{4}{20}

To simplify this expression, we can multiply the numerator (4) by 240 and then divide by the denominator (20):

Number of nickels = \frac{4 \* 240}{20}

Number of nickels = \frac{960}{20}

Number of nickels = 48

So, Eric has 48 nickels in his collection.

Calculating the Number of Quarters

We know that the rest of the coins in Eric's collection are quarters. To find the number of quarters, we can subtract the total number of pennies and nickels from the total number of coins.

Number of quarters = Total number of coins - Number of pennies - Number of nickels

Given that Eric has 240 coins in his collection, 132 pennies, and 48 nickels, we can substitute these values into the equation:

Number of quarters = 240 - 132 - 48

Number of quarters = 60

So, Eric has 60 quarters in his collection.

Conclusion

In this problem, we used fractions to calculate the number of pennies, nickels, and quarters in Eric's collection. We found that Eric has 132 pennies, 48 nickels, and 60 quarters. By subtracting the total number of pennies and nickels from the total number of coins, we were able to determine the number of quarters in Eric's collection.

Key Takeaways

To calculate the number of coins of a particular type, we can multiply the total number of coins by the fraction representing the proportion of that type of coin.
To find the number of quarters, we can subtract the total number of pennies and nickels from the total number of coins.
Fractions can be used to represent proportions and can be manipulated using basic arithmetic operations.

Real-World Applications

This problem can be applied to real-world situations where we need to calculate proportions or percentages. For example, in business, we may need to calculate the proportion of sales from different product categories. In finance, we may need to calculate the proportion of investments in different asset classes. In science, we may need to calculate the proportion of a particular substance in a mixture.

Practice Problems

A bakery sells a total of 240 loaves of bread per day. ${$ \frac{3}{5}$}$ of the loaves are whole wheat, and ${$ \frac{1}{5}$}$ are rye. What is the number of rye loaves sold per day?
A company has a total of 480 employees. ${$ \frac{2}{5}$}$ of the employees are in the sales department, and ${$ \frac{1}{5}$}$ are in the marketing department. What is the number of employees in the marketing department?
A school has a total of 360 students. ${$ \frac{3}{4}$}$ of the students are in the 9th grade, and ${$ \frac{1}{4}$}$ are in the 10th grade. What is the number of students in the 10th grade?
Q&A: Eric's Coin Collection =============================

Q: What is the total number of coins in Eric's collection?

A: Eric has a total of 240 coins in his collection.

Q: What is the proportion of pennies in Eric's collection?

A: The proportion of pennies in Eric's collection is ${$ \frac{11}{20}$}$.

Q: How many pennies are in Eric's collection?

A: To find the number of pennies, we can multiply the total number of coins by the proportion of pennies. This gives us:

Number of pennies = 240 \* \frac{11}{20}

Number of pennies = \frac{11 \* 240}{20}

Number of pennies = \frac{2640}{20}

Number of pennies = 132

So, Eric has 132 pennies in his collection.

Q: What is the proportion of nickels in Eric's collection?

A: The proportion of nickels in Eric's collection is ${$ \frac{4}{20}$}$.

Q: How many nickels are in Eric's collection?

A: To find the number of nickels, we can multiply the total number of coins by the proportion of nickels. This gives us:

Number of nickels = 240 \* \frac{4}{20}

Number of nickels = \frac{4 \* 240}{20}

Number of nickels = \frac{960}{20}

Number of nickels = 48

So, Eric has 48 nickels in his collection.

Q: What is the proportion of quarters in Eric's collection?

A: Since the rest of the coins in Eric's collection are quarters, the proportion of quarters is 1 minus the sum of the proportions of pennies and nickels.

Proportion of quarters = 1 - (\frac{11}{20} + \frac{4}{20})

Proportion of quarters = 1 - \frac{15}{20}

Proportion of quarters = \frac{5}{20}

Proportion of quarters = \frac{1}{4}

Q: How many quarters are in Eric's collection?

A: To find the number of quarters, we can multiply the total number of coins by the proportion of quarters. This gives us:

Number of quarters = 240 \* \frac{1}{4}

Number of quarters = \frac{1 \* 240}{4}

Number of quarters = \frac{240}{4}

Number of quarters = 60

So, Eric has 60 quarters in his collection.

Q: How did you find the number of quarters in Eric's collection?

A: We found the number of quarters by subtracting the total number of pennies and nickels from the total number of coins.

Number of quarters = Total number of coins - Number of pennies - Number of nickels

Number of quarters = 240 - 132 - 48

Number of quarters = 60

Q: What are some real-world applications of this problem?

A: This problem can be applied to real-world situations where we need to calculate proportions or percentages. For example, in business, we may need to calculate the proportion of sales from different product categories. In finance, we may need to calculate the proportion of investments in different asset classes. In science, we may need to calculate the proportion of a particular substance in a mixture.

Q: What are some practice problems that can help reinforce this concept?

A: Here are a few practice problems that can help reinforce this concept:

A bakery sells a total of 240 loaves of bread per day. ${$ \frac{3}{5}$}$ of the loaves are whole wheat, and ${$ \frac{1}{5}$}$ are rye. What is the number of rye loaves sold per day?
A company has a total of 480 employees. ${$ \frac{2}{5}$}$ of the employees are in the sales department, and ${$ \frac{1}{5}$}$ are in the marketing department. What is the number of employees in the marketing department?
A school has a total of 360 students. ${$ \frac{3}{4}$}$ of the students are in the 9th grade, and ${$ \frac{1}{4}$}$ are in the 10th grade. What is the number of students in the 10th grade?