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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
To understand what [tex]\( x \)[/tex] represents in the given equations, let's break down each of the salary options provided:

1. First Salary Option:
[tex]\[ y = 9x + 50 \][/tex]
- In this equation, [tex]\( y \)[/tex] is the total weekly earnings.
- Jeremiah earns [tex]\( \$9 \)[/tex] per hour.
- He also receives a [tex]\( \$50 \)[/tex] weekly bonus for opening the store.
- Therefore, [tex]\( 9x \)[/tex] represents the earnings from working for [tex]\( x \)[/tex] hours at [tex]\( \$9 \)[/tex] per hour.

2. Second Salary Option:
[tex]\[ y = 10x \][/tex]
- In this equation, [tex]\( y \)[/tex] is again the total weekly earnings.
- Jeremiah earns [tex]\( \$10 \)[/tex] per hour.
- Here, [tex]\( 10x \)[/tex] represents the earnings from working for [tex]\( x \)[/tex] hours at [tex]\( \$10 \)[/tex] per hour, with no additional bonus.

Since [tex]\( y \)[/tex] in both equations represents the total amount earned each week, and [tex]\( x \)[/tex] is the variable being multiplied by the hourly rate (either [tex]\( 9 \)[/tex] or [tex]\( 10 \)[/tex]), [tex]\( x \)[/tex] clearly represents the number of hours worked per week.

Therefore, the correct answer is:
- The number of hours worked per week.

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