A collection of dimes and quarters is worth .55 – A collection of dimes and quarters, valued at $9.55, presents an intriguing mathematical puzzle. This exploration delves into the monetary value, coin count, and potential combinations that contribute to this specific worth, offering a comprehensive analysis of this intriguing numismatic quandary.
The total value of the collection, $9.55, comprises a combination of dimes (each worth $0.10) and quarters (each worth $0.25). Determining the precise number of coins and their respective denominations requires a systematic approach, considering various coin combinations and alternative calculation methods.
Monetary Value: A Collection Of Dimes And Quarters Is Worth .55
The total value of the collection of dimes and quarters is $9.55. This is the sum of the individual values of the dimes and quarters in the collection.
Each dime is worth $0.10, and each quarter is worth $0.25. Therefore, the total value of the dimes in the collection is $0.10 x the number of dimes, and the total value of the quarters in the collection is $0.25 x the number of quarters.
Coin Count
To calculate the number of dimes and quarters in the collection, we can use the following equations:
Number of dimes = Total value of dimes / Value of a dime ($0.10)
Number of quarters = Total value of quarters / Value of a quarter ($0.25)
Using these equations, we can calculate that there are 95 dimes and 20 quarters in the collection.
| Dime Count | Quarter Count |
|---|---|
| 95 | 20 |
Coin Combinations
There are many possible combinations of dimes and quarters that add up to $9. 55. Some of these combinations are shown in the following table:
| Dime Count | Quarter Count | Total Value |
|---|---|---|
| 95 | 0 | $9.50 |
| 90 | 5 | $9.55 |
| 85 | 10 | $9.55 |
| 80 | 15 | $9.55 |
| 75 | 20 | $9.55 |
Alternative Calculations
There are several alternative methods for calculating the number of dimes and quarters in the collection. One method is to use the following equations:
Number of dimes = (Total value of collection
Total value of quarters) / Value of a dime ($0.10)
Number of quarters = Total value of quarters / Value of a quarter ($0.25)
Another method is to use the following steps:
- Divide the total value of the collection by the value of a quarter ($0.25) to get the number of quarters.
- Multiply the number of quarters by the value of a quarter ($0.25) to get the total value of the quarters.
- Subtract the total value of the quarters from the total value of the collection to get the total value of the dimes.
- Divide the total value of the dimes by the value of a dime ($0.10) to get the number of dimes.
Clarifying Questions
What is the total number of coins in the collection?
The total number of coins can vary depending on the combination of dimes and quarters. Without specific information on the coin count, it is not possible to determine the exact number.
Are there any other possible combinations of dimes and quarters that add up to $9.55?
Yes, there are multiple combinations of dimes and quarters that can add up to $9.55. The table in the Artikel presents some possible combinations, but there may be others.
What is the significance of studying coin combinations?
Studying coin combinations helps us understand the mathematical relationships between different coin denominations and their collective value. It also provides insights into the principles of monetary systems and the practical applications of mathematics in everyday life.
