A cashier earns $7 an hour. If [tex]$x$[/tex] is the number of hours worked, which function represents the cashier's earnings?
A. [tex]$y=7x$[/tex]
B. [tex]$y=x^7$[/tex]
C. [tex]$y=\frac{7}{x}$[/tex]
D. [tex]$y=7$[/tex]
Answer (2)
The cashier earns 7 p er h o u r , an d x$ represents the number of hours worked.
The total earnings, y , is calculated by multiplying the hourly rate by the number of hours worked: y = 7 × x .
The function representing the cashier's earnings is y = 7 x .
Therefore, the answer is y = 7 x .
Explanation
Understanding the Problem Let's analyze the problem. We are given that a cashier earns 7 p er h o u r . W e n ee d t o f in d a f u n c t i o n t ha t re p rese n t s t h ec a s hi e r ′ se a r nin g s , d e n o t e d a s y , ba se d o n t h e n u mb ero f h o u rs w or k e d , d e n o t e d a s x$.
Formulating the Equation Since the cashier earns a fixed amount for each hour worked, we can express the total earnings as the product of the hourly rate and the number of hours worked. This can be written as: y = 7 × x where:
y represents the total earnings
7 is the hourly rate
x is the number of hours worked
Identifying the Correct Function Now, let's compare this equation with the given options:
y = 7 x
y = x 7
y = x 7
y = 7
The equation y = 7 x matches our derived equation.
Final Answer Therefore, the function that represents the cashier's earnings is y = 7 x .
Examples
Imagine you're saving up to buy a new video game that costs $63. If you earn $7 per hour as a cashier, this problem helps you calculate how many hours you need to work to afford the game. By understanding the relationship between your hourly wage and the number of hours you work, you can plan your work schedule to reach your savings goal. This concept is useful for budgeting, setting financial goals, and making informed decisions about your time and money.
The function that represents the cashier's earnings, where the cashier earns 7 p er h o u r f or x h o u rs w or k e d , i s g i v e nb y t h ee q u a t i o n y = 7x . T h u s , t h ecorrec t o pt i o ni s A : y=7x$. This simple relationship shows that total earnings are directly proportional to the number of hours worked.
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