Final answer:
By defining variables for the amounts of each bill Janice has, setting up an equation based on the total amount of money, and then solving for the variable, you can determine that she has 3 ten-dollar bills, 9 one-dollar bills, and 7 five-dollar bills. However, only whole numbers of bills are possible, and since 7 is not an option, there may be a need to reevaluate the approach if this discrepancy arises in a real scenario.
Step-by-step explanation:
How to Determine the Number of Five-Dollar Bills
To solve the problem, let's use algebra and represent the number of ten-dollar bills as t. Since Janice has 3 times as many one-dollar bills as ten-dollar bills, we can say she has 3t one-dollar bills. She has 2 fewer five-dollar bills than one-dollar bills, hence she would have (3t - 2) five-dollar bills.
Now, let's translate the information into a mathematical equation that represents the total amount of money Janice has:
- 10 (dollar bills) × t (number of ten-dollar bills) = 10t (total value of ten-dollar bills)
- 1 (dollar bill) × 3t (number of one-dollar bills) = 3t (total value of one-dollar bills)
- 5 (dollar bills) × (3t - 2) (number of five-dollar bills) = 15t - 10 (total value of five-dollar bills)
Adding these up gives us Janice's total:
10t + 3t + 15t - 10 = 74, which simplifies to 28t - 10 = 74. Solving this equation for t gives us t = 3. Therefore, Janice has (3t - 2) five-dollar bills, which equals 7. However, 7 is not an option given in the question, indicating a possible miscalculation. Upon reassessing the options provided, we see that the closest number to 7 is 6, which may suggest reevaluating the equation or verifying if the options or the initial equation have been stated correctly.