Final answer:
To solve the problem, we used variables to represent the number of quarters and dimes, set up an equation based on their values, and solved for the number of each coin. Francie has 19 quarters and 16 dimes.
Step-by-step explanation:
The question asks us to determine the number of dimes and quarters Francie has, given that she has a total of $6.35 in those coins and that the number of dimes is 3 less than the number of quarters.
Step-by-Step Solution:
- Let's assign variables: Let q represent the number of quarters. Since we are told the number of dimes is 3 less than the number of quarters, d, the number of dimes, will be q - 3.
- We need to write an equation that represents the total value of the dimes and quarters. We know that each quarter is worth $0.25 and each dime is worth $0.10. So, the total value of the quarters is 0.25q and the total value of the dimes is 0.10(q - 3).
- Now we can write an equation to represent the total amount of money Francie has: 0.25q + 0.10(q - 3) = 6.35.
- Expanding the equation, we get 0.25q + 0.10q - 0.30 = 6.35.
- Combining like terms, we get 0.35q = 6.65.
- Dividing both sides by 0.35 gives us q = 19. Thus, Francie has 19 quarters.
- To find the number of dimes, we substitute q into the dimes equation: d = q - 3, which gives us d = 19 - 3 = 16. So, Francie has 16 dimes.
Francie has 19 quarters and 16 dimes.