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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

1 answer

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.