Let's break down the problem to identify the correct system of equations that models Jody's work hours and earnings.
First, we define the variables:
- Let [tex]\( x \)[/tex] be the number of hours Jody babysat.
- Let [tex]\( y \)[/tex] be the number of hours she did yardwork.
Given conditions:
1. Jody worked a total of 34 hours combining babysitting and yardwork. This can be written as:
[tex]\[
x + y = 34
\][/tex]
2. Jody earns [tex]\(\$10\)[/tex] per hour for babysitting and [tex]\(\$15\)[/tex] per hour for yardwork. The total earnings for the week were
[tex]\(\$410\)[/tex]. This can be written as:
[tex]\[
10x + 15y = 410
\][/tex]
Now let's match these equations to the given options:
A.
[tex]\[
x + y = 34
\][/tex]
[tex]\[
10x + 15y = 410
\][/tex]
B.
[tex]\[
x + y = 410
\][/tex]
[tex]\[
10x + 15y = 34
\][/tex]
C.
[tex]\[
x + y = 34
\][/tex]
[tex]\[
15x + 10y = 410
\][/tex]
D.
[tex]\[
x + y = 410
\][/tex]
[tex]\[
15x + 10y = 34
\][/tex]
Analyzing these options, only option A represents the correct system of equations matching our conditions:
[tex]\[
x + y = 34
\][/tex]
[tex]\[
10x + 15y = 410
\][/tex]
Therefore, the correct answer is option A.
