Select the correct answer.

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

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]



Answer :

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]