Finding the Number of Dimes

Oct 13, 2025 by leolavanderia.com.br 90 views

Introduction

In this problem, we are given that a boy has a total of $2.25 in his coin collection, consisting of nickels and dimes. We are also told that there are twice as many dimes as nickels. Let's use algebra to solve for the number of nickels and dimes in his collection.

Let's Define the Variables

Let $x$ be the number of nickels. Since there are twice as many dimes as nickels, the number of dimes is $2x$ .

The Value of the Coins

The value of a nickel is $0.05, and the value of a dime is $0.10. We can set up an equation to represent the total value of the coins:

0.05x + 0.10(2x) = 2.25

Simplifying the Equation

We can simplify the equation by combining like terms:

0.05x + 0.20x = 2.25

0.25x = 2.25

Solving for x

To solve for $x$ , we can divide both sides of the equation by $0.25$ :

x = \frac{2.25}{0.25}

x = 9

Finding the Number of Dimes

Since there are twice as many dimes as nickels, the number of dimes is $2x$ :

2x = 2(9)

2x = 18

Conclusion

In conclusion, the boy has 9 nickels and 18 dimes in his coin collection. This problem demonstrates how algebra can be used to solve real-world problems involving coins and currency.

Additional Examples

Here are a few more examples of how algebra can be used to solve problems involving coins and currency:

A store sells a total of 250 items, consisting of shirts and pants. If the number of shirts is 30 more than the number of pants, how many of each item does the store sell?
A bank has a total of $10,000 in its vault, consisting of $5 and $10 bills. If the number of $10 bills is 2 times the number of $5 bills, how many of each bill does the bank have?
A candy store sells a total of 500 pieces of candy, consisting of gummies and sour candies. If the number of gummies is 3 times the number of sour candies, how many of each type of candy does the store sell?

Real-World Applications

Algebra has many real-world applications, including:

Finance: Algebra is used to calculate interest rates, investments, and loans.
Science: Algebra is used to model population growth, chemical reactions, and physical systems.
Engineering: Algebra is used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Computer Science: Algebra is used to develop algorithms and solve problems in computer science.

Conclusion

Q: What is the value of a nickel and a dime?

A: The value of a nickel is $0.05, and the value of a dime is $0.10.

Q: How many nickels and dimes does the boy have in total?

A: The boy has a total of $2.25 in his coin collection. Since the value of a nickel is $0.05 and the value of a dime is $0.10, we can set up an equation to represent the total value of the coins:

0.05x + 0.10(2x) = 2.25

Q: How do we simplify the equation?

A: We can simplify the equation by combining like terms:

0.05x + 0.20x = 2.25

0.25x = 2.25

Q: How do we solve for x?

A: To solve for $x$ , we can divide both sides of the equation by $0.25$ :

x = \frac{2.25}{0.25}

x = 9

Q: How many dimes does the boy have?

A: Since there are twice as many dimes as nickels, the number of dimes is $2x$ :

2x = 2(9)

2x = 18

Q: What is the ratio of nickels to dimes?

A: The ratio of nickels to dimes is 1:2, since there are twice as many dimes as nickels.

Q: How can we use algebra to solve other coin problems?

A: Algebra can be used to solve a wide range of coin problems, including those involving different denominations of coins, different numbers of coins, and different total values. By using algebra, we can model real-world situations and make predictions about the outcomes.

Q: What are some real-world applications of algebra?

A: Algebra has many real-world applications, including:

Finance: Algebra is used to calculate interest rates, investments, and loans.
Science: Algebra is used to model population growth, chemical reactions, and physical systems.
Engineering: Algebra is used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Computer Science: Algebra is used to develop algorithms and solve problems in computer science.

Q: How can I practice using algebra to solve coin problems?

A: You can practice using algebra to solve coin problems by working through examples and exercises, such as:

A store sells a total of 250 items, consisting of shirts and pants. If the number of shirts is 30 more than the number of pants, how many of each item does the store sell?
A bank has a total of $10,000 in its vault, consisting of $5 and $10 bills. If the number of $10 bills is 2 times the number of $5 bills, how many of each bill does the bank have?
A candy store sells a total of 500 pieces of candy, consisting of gummies and sour candies. If the number of gummies is 3 times the number of sour candies, how many of each type of candy does the store sell?

Q: Where can I find more information about algebra and coin problems?

A: You can find more information about algebra and coin problems by:

Consulting algebra textbooks and online resources
Working with a tutor or teacher
Practicing with online exercises and examples
Joining online communities and forums for math enthusiasts