To find the correct system of equations that models the given situation, we need to translate the problem's information into mathematical equations.
1. Total Hours Worked:
Jody worked a total of 34 hours this week. If [tex]\( x \)[/tex] represents the number of hours she babysat and [tex]\( y \)[/tex] represents the number of hours she did yardwork, the equation representing the total hours worked is:
[tex]\[
x + y = 34
\][/tex]
2. Total Earnings:
Jody earned a total of \[tex]$410 this week. She earns \$[/tex]10 per hour for babysitting and \$15 per hour for doing yardwork. Therefore, the equation representing her total earnings is:
[tex]\[
10x + 15y = 410
\][/tex]
The correct system of equations that models this situation is:
[tex]\[
\begin{cases}
x + y = 34 \\
10x + 15y = 410
\end{cases}
\][/tex]
Among the given options:
A.
[tex]\[
\begin{cases}
x + y = 34 \\
10x + 15y = 410
\end{cases}
\][/tex]
B.
[tex]\[
\begin{cases}
x + y = 410 \\
10x + 15y = 34
\end{cases}
\][/tex]
C.
[tex]\[
\begin{cases}
x + y = 34 \\
15x + 10y = 410
\end{cases}
\][/tex]
D.
[tex]\[
\begin{cases}
x + y = 410 \\
15x + 10y = 34
\end{cases}
\][/tex]
The correct answer is:
[tex]\[ A \][/tex]
[tex]\[
\begin{cases}
x + y = 34 \\
10x + 15y = 410
\end{cases}
\][/tex]
