Question

Use the guess and check method to determine if who has the correct solution.

Jane has $50 in her wallet. The bills are worth either $5 or $1. There are 18 bills total.



Bodhi says Jane has 6 five dollar bills and 10 one dollar bills.

Manny says Jane has 8 five dollar bills and 10 one dollar bills.


Use the guess and check method to determine if who has the correct solution.

Jane has $50 in her wallet. The bills are worth either $5 or $1. There are 18 bills total.



Bodhi says Jane has 6 five dollar bills and 10 one dollar bills.

Manny says Jane has 8 five dollar bills and 10 one dollar bills.


Bohdi


Manny

Answer 1

To solve this problem, we will use the guess and check method to evaluate the claims made by Bodhi and Manny against the conditions given.

### Given Information:

1. Total amount of money: $50
2. Total number of bills: 18
3. Bills are either $5 or $1.

Let:
- \( x \) = the number of $5 bills
- \( y \) = the number of $1 bills

We have the following equations based on the information:

1. \( x + y = 18 \) (equation for the total number of bills)
2. \( 5x + 1y = 50 \) (equation for the total amount of money)

### Checking Bodhi's Claim: 6 five dollar bills and 10 one dollar bills

Bodhi's claim:
- \( x = 6 \)
- \( y = 10 \)

We will plug these values into the equations to check their validity.

1. Checking the total number of bills:
\[
x + y = 6 + 10 = 16 \quad \text{(Not equal to 18)}
\]

2. Checking the total amount of money:
\[
5x + 1y = 5(6) + 1(10) = 30 + 10 = 40 \quad \text{(Not equal to 50)}
\]

So, Bodhi is incorrect.

### Checking Manny's Claim: 8 five dollar bills and 10 one dollar bills

Manny's claim:
- \( x = 8 \)
- \( y = 10 \)

We will plug these values into the equations to check their validity.

1. Checking the total number of bills:
\[
x + y = 8 + 10 = 18 \quad \text{(This is correct)}
\]

2. Checking the total amount of money:
\[]
5x + 1y = 5(8) + 1(10) = 40 + 10 = 50 \quad \text{(This is correct)}
\]

### Conclusion:
- Bodhi is incorrect.
- Manny is correct.

Thus, Manny has the correct solution: Jane has 8 five dollar bills and 10 one dollar bills.