Final answer:
Using a system of equations, we find that Francie has 14 quarters and 15 dimes given that she has a total of $5.00 in dimes and quarters, with the dimes being 1 more than the number of quarters. None of the provided options match this solution.
Step-by-step explanation:
The question is asking us to determine how many dimes and quarters Francie has if she has $5.00 in total, with the number of dimes being 1 more than the number of quarters. We can solve this problem using a system of equations. Let's define Q as the number of quarters and D as the number of dimes. The value of a dime is 10 cents, and the value of a quarter is 25 cents. Since 1 dollar equals 100 pennies, we have two equations:
- 10D + 25Q = 500 (because Francie has $5.00, which is 500 cents)
- D = Q + 1 (because there is one more dime than quarters)
Now we substitute the second equation into the first to find the number of quarters:
- 10(Q + 1) + 25Q = 500
- 10Q + 10 + 25Q = 500
- 35Q + 10 = 500
- 35Q = 490
- Q = 14
Now that we know Q is 14, we can find D by plugging Q back into the second equation:
- D = Q + 1
- D = 14 + 1
- D = 15
Therefore, Francie has 14 quarters and 15 dimes. This means none of the provided options (a, b, c, or d) are correct.