Gabe has 60 coins consisting of quarters and dimes – Gabe, a young numismatist, finds himself in possession of an intriguing collection: 60 coins composed solely of quarters and dimes. Embarking on a mathematical quest, we delve into the realm of coin combinations, seeking to unravel the optimal arrangement that maximizes their collective value.
As we analyze various combinations, we uncover the intricacies of coin denominations, their respective values, and the impact they have on the overall worth of Gabe’s collection. Through a series of calculations and visual representations, we unravel the secrets behind these monetary mosaics.
Coin Combinations: Gabe Has 60 Coins Consisting Of Quarters And Dimes
There are multiple combinations of quarters and dimes that add up to 60 coins. The following table lists some possible combinations along with their corresponding total value:
| Quarters | Dimes | Total Coins | Total Value |
|---|---|---|---|
| 24 | 36 | 60 | $15 |
| 30 | 30 | 60 | $15 |
| 36 | 24 | 60 | $15 |
| 42 | 18 | 60 | $15 |
| 48 | 12 | 60 | $15 |
| 54 | 6 | 60 | $15 |
Value of Coins
Assuming quarters are worth 25 cents each and dimes are worth 10 cents each, the total value of all 60 coins is $15.
Total Value = (Number of Quarters
- Value of Quarter) + (Number of Dimes
- Value of Dime)
Total Value = (24
- $0.25) + (36
- $0.10)
Total Value = $6 + $3.60
Total Value = $15
Number of Quarters and Dimes
The combination that results in the highest total value is 24 quarters and 36 dimes. This combination has a total value of $15.
Alternative Combinations
There are other combinations of quarters and dimes that have the same total value as the combination with the highest total value. For example, the following combinations also have a total value of $15:
- 30 quarters and 30 dimes
- 36 quarters and 24 dimes
- 42 quarters and 18 dimes
- 48 quarters and 12 dimes
- 54 quarters and 6 dimes
Visual Representation
The following bar graph illustrates the distribution of quarters and dimes in the combination with the highest total value:
Clarifying Questions
How many quarters does Gabe have?
The number of quarters Gabe has is not specified in the given information.
What is the total value of Gabe’s coins?
The total value of Gabe’s coins depends on the specific combination of quarters and dimes he has, which is not provided in the given information.
Can Gabe exchange his coins for a dollar?
Yes, Gabe can exchange his coins for a dollar if he has the right combination of quarters and dimes. For example, 4 quarters and 20 dimes add up to 1 dollar.
