Select the correct answer.

Question

During the summer, Jody earns $10 per hour babysitting and $15 per hour doing yardwork. This week she worked 34 hours and earned $410. If x represents the number hours she babysat and y represents the number of hours she did yardwork, which system of equations models this situation?

A.
x + y = 34
10x + 15y = 410
B.
x + y = 410
10x + 15y = 34
C.
x + y = 34
15x + 10y = 410
D.
x + y = 410
15x + 10y = 34

Answer 1

To solve the problem, we need to establish the two equations based on the information given.

1. The total number of hours worked by Jody is 34. This can be expressed as: \[ x + y = 34 \] where \( x \) represents the hours she babysat and \( y \) represents the hours she did yardwork.

2. The total earnings from babysitting at $10 per hour and yardwork at $15 per hour sums to $410. This can be expressed as: \[ 10x + 15y = 410 \]

Putting these two equations together forms the system: \[ \begin{align*}

1. & \quad x + y = 34 \
2. & \quad 10x + 15y = 410 \end{align*} \]

Now, looking at the answer choices provided:

• A. \( x + y = 34 \) and \( 10x + 15y = 410 \) (This matches our derived equations.)
• B. \( x + y = 410 \) and \( 10x + 15y = 34 \) (Incorrect)
• C. \( x + y = 34 \) and \( 15x + 10y = 410 \) (Incorrect)
• D. \( x + y = 410 \) and \( 15x + 10y = 34 \) (Incorrect)

Thus, the correct answer is: A. \( x + y = 34 \) \( 10x + 15y = 410 \)