Let's verify the claims made by Bosnian and Manny about the bills that Jane has.
Let:
- \( x \) be the number of $5 bills.
- \( y \) be the number of $1 bills.
From the problem, we know three pieces of information:
-
The total number of bills is 18. \[ x + y = 18 \]
-
The total amount of money is $50. \[ 5x + 1y = 50 \]
We can now analyze each person's claim to see if either of them is correct.
Bosnian's Claim:
Bosnian claims Jane has 6 five dollar bills and 10 one dollar bills.
- Here, \( x = 6 \) and \( y = 10 \).
Let's check if this satisfies our equations:
- Total number of bills: \[ x + y = 6 + 10 = 16 \quad (\text{not } 18) \] Thus, Bosnian's claim is not correct.
Manny's Claim:
Manny claims Jane has 8 five dollar bills and 10 one dollar bills.
- Here, \( x = 8 \) and \( y = 10 \).
Now, let's check this:
-
Total number of bills: \[ x + y = 8 + 10 = 18 \quad (\text{correct}) \]
-
Total amount of money: \[ 5x + 1y = 5(8) + 1(10) = 40 + 10 = 50 \quad (\text{correct}) \]
Since both conditions are satisfied for Manny's claim, Manny's assertion is correct.
Conclusion:
Jane has 8 five dollar bills and 10 one dollar bills. Bosnian's claim is incorrect while Manny's claim is correct.