Question

Question 24
A student has two part-time jobs: babysitting and tutoring. The student earns an hourly wage at each job.

*On Monday, the student earned a total of $165 for 4 hours babysitting and 3 hours of tutoring.
*On Tuesday, the student earned a total of $115 for 3 hours babysitting and 2 hours tutoring.

Which of the following systems of equations can be used to find x, the student's hourly wage for babysitting, and y, the student's hourly wage for tutoring?
*
1 point

A 3x+2y=165
4x+3y = 115

B 4x+3y=165
4x+2y = 115

C 3x+4y=165
2x+3y = 115

Answer 1

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:

1. On Monday, the student worked 4 hours babysitting and 3 hours tutoring, earning a total of $165. This can be modeled by the equation:
\[
4x + 3y = 165
\]

2. 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.