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At his new job, Jeremiah can choose an hourly rate of [tex]$\$[/tex]9[tex]$ plus a $[/tex]\[tex]$50$[/tex] weekly bonus for opening the store, or an hourly rate of [tex]$\$[/tex]10[tex]$ per hour with no opening bonus. The equations model his salary options.

\[
\begin{array}{l}
y = 9x + 50 \\
y = 10x
\end{array}
\]

What does $[/tex]x$ represent?

A. the number of times he opened the store
B. the number of hours worked per week
C. the total amount he earns each week
D. the amount of money earned per day



Answer :

GinnyAnswer
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.

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