Certainly! To determine what [tex]\( x \)[/tex] represents in the given equations, let's carefully analyze each equation and the context of Jeremiah's job options.
The first salary option is represented by the equation:
[tex]\[ y = 9x + 50 \][/tex]
In this equation:
- [tex]\( y \)[/tex] represents Jeremiah's total salary.
- [tex]\( 9x \)[/tex] represents the earnings from his hourly rate, where [tex]\( x \)[/tex] is the number of hours worked, and he earns \[tex]$9 per hour.
- The additional \$[/tex]50 is a weekly bonus for opening the store.
So, this equation tells us Jeremiah's total weekly salary comes from two components: his hourly wage earnings and a fixed weekly bonus.
The second salary option is represented by the equation:
[tex]\[ y = 10x \][/tex]
In this equation:
- [tex]\( y \)[/tex] once again represents Jeremiah's total salary.
- [tex]\( 10x \)[/tex] represents the earnings from his hourly rate, where [tex]\( x \)[/tex] is the number of hours worked, and he earns \$10 per hour.
Both equations are modeling Jeremiah's total weekly salary ([tex]\( y \)[/tex]) based on the number of hours worked ([tex]\( x \)[/tex]). Since [tex]\( x \)[/tex] is used to calculate the total earnings from the hourly wage in both equations, it indicates that [tex]\( x \)[/tex] is the variable representing the number of hours worked per week.
Therefore, the correct interpretation of [tex]\( x \)[/tex] is:
The number of hours worked per week.
