To find the correct system of equations to model the student's earnings from babysitting and tutoring, we need to set up the equations based on the information given.
Let:
- \( x \) be the hourly wage for babysitting.
- \( y \) be the hourly wage for tutoring.
From the problem statement:
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On Monday, the student worked 4 hours babysitting and 3 hours tutoring, earning a total of $165. This can be modeled by the equation: \[ 4x + 3y = 165 \]
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On Tuesday, the student worked 3 hours babysitting and 2 hours tutoring, earning a total of $115. This can be modeled by the equation: \[ 3x + 2y = 115 \]
Therefore, the system of equations that can be used to find \( x \) and \( y \) is: \[ \begin{align*} 4x + 3y &= 165 \ 3x + 2y &= 115 \ \end{align*} \]
Looking at the options provided:
- Option A: \( 3x + 2y = 165 \) and \( 4x + 3y = 115 \) (Incorrect)
- Option B: \( 4x + 3y = 165 \) and \( 4x + 2y = 115 \) (Incorrect)
- Option C: \( 3x + 4y = 165 \) and \( 2x + 3y = 115 \) (Incorrect)
None of the options provided match the correct system of equations derived from the problem. The correct system should be:
- \( 4x + 3y = 165 \)
- \( 3x + 2y = 115 \)
If this was an answer choice, it would be the correct one.