Final answer:
The correct answer is (a) Quarters: 30, Dimes: 15, Nickels: 40. By assigning the number of dimes as 'd,' the number of quarters as '2d', and calculating the remaining coins as nickels to sum up to 85, we can determine that option (a) satisfies the conditions given.
Step-by-step explanation:
The question involves determining the correct number of quarters, dimes, and nickels given certain conditions. We are told there are twice as many quarters as dimes and that the total number of coins is 85. Let's denote the number of dimes as d. Therefore, the number of quarters will be 2d (since there are twice as many quarters as dimes). The number of nickels will be 85 - d - 2d because the total number of coins is 85.
We can set up an equation to find the values:
- d + 2d + (85 - d - 2d) = 85
- So, 3d = 85
- d = 85 / 3
- d = 28.333
Since we can't have a fraction of a coin, option (a), with 30 quarters, 15 dimes, and 40 nickels, can be the only solution because:
- Number of dimes d is 15
- Number of quarters 2d is (2 * 15) = 30
- Number of nickels is (85 - 15 - 30) = 40
Checking each option, option (a) adheres to the given ratio and sums up to the total number of coins, thereby making it the correct answer.