Final answer:
By setting up and solving a system of equations, we find that Bob has 24 dimes and 2 nickels based on the conditions given; however, this correct answer is not listed among the provided choices, indicating a potential error in the question or choices.
Step-by-step explanation:
To solve the problem of how many dimes and nickels Bob has, we must set up a system of equations based on the given information. First, we know that the value of the dimes and nickels adds up to $2.50, and that a dime is worth 10 cents, and a nickel is worth 5 cents. Secondly, we are told that the number of dimes is four more than ten times the number of nickels.
Let's say N represents the number of nickels and D represents the number of dimes. We can translate the problem into the following equations:
- 10D + 5N = 250 (Because the total amount in cents is 250)
- D = 10N + 4 (The number of dimes is ten times the number of nickels plus four)
Substituting the second equation into the first equation gives us:
- 10(10N + 4) + 5N = 250
- 100N + 40 + 5N = 250
- 105N + 40 = 250
- 105N = 250 - 40
- 105N = 210
- N = 210 / 105
- N = 2
Now we know that Bob has 2 nickels. To find the number of dimes, we'll use the second equation:
- D = 10(2) + 4
- D = 20 + 4
- D = 24
Therefore, Bob has 24 dimes and 2 nickels, which is not listed among the provided choices. There appears to be a mistake in the initial problem or choices given because our calculated answer does not match the options.