Theresa has $26 in her wallet. The bills are worth either $5 or $1. There are 14 bills total.

Question

Bodhi says Theresa has 3 five dollar bills and 11 one dollar bills.

Manny says Theresa has 2 five dollar bills and 12 one dollar bills.

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

Theresa has $26 in her wallet. The bills are worth either $5 or $1. There are 14 bills total.



Bodhi says Theresa has 3 five dollar bills and 11 one dollar bills.

Manny says Theresa has 2 five dollar bills and 12 one dollar bills.

Bohdi

Manny

Answer 1

To determine who is correct between Bodhi and Manny regarding the bills that Theresa has, we will check the suggested combinations of bills against the conditions given:

1. The total amount of money must be $26.
2. The total number of bills must be 14.

Bodhi's Claim:

• 3 five dollar bills
• 11 one dollar bills

We will calculate the total amount and total number of bills:

1. Total amount from the five dollar bills: \(3 \times 5 = 15\)
2. Total amount from the one dollar bills: \(11 \times 1 = 11\)
3. Total amount: \(15 + 11 = 26\)
4. Total number of bills: \(3 + 11 = 14\)

Bodhi's claim satisfies both the total amount and the total number of bills.

Manny's Claim:

• 2 five dollar bills
• 12 one dollar bills

We will do the same calculations:

1. Total amount from the five dollar bills: \(2 \times 5 = 10\)
2. Total amount from the one dollar bills: \(12 \times 1 = 12\)
3. Total amount: \(10 + 12 = 22\)
4. Total number of bills: \(2 + 12 = 14\)

Manny's claim does not satisfy the total amount condition (the total amount is $22, not $26).

Conclusion: Bodhi's claim (3 five dollar bills and 11 one dollar bills) is correct. Manny's claim is incorrect.