Final answer:
To find the value of the quarters when their number is four times that of the dimes, we express the total value in terms of the number of quarters and their respective coin value, solving for the total value of quarters as a portion of $X.
Step-by-step explanation:
To solve the problem where the number of dimes is 1/4 the number of quarters, and the total value of dimes and quarters is $X, we need to first establish a relationship between the numbers of each type of coin and use the values of the coins (10 cents for a dime and 25 cents for a quarter) to express the total value.
Let's assume there are q quarters. According to the problem, there are d dimes and d = (1/4) * q. The total value of the quarters is q * $0.25, and the total value of the dimes is d * $0.10. Using the information provided, we can create the equation:
0.25q + 0.10d = $X
We know that d = (1/4) * q, so we substitute this into the equation:
0.25q + 0.10((1/4)q) = $X
which simplifies to:
0.25q + 0.025q = $X
0.275q = $X
Therefore, the value of quarters in terms of $X is:
0.275q = $X
This means that the value of the quarters is $X divided by 0.275.