Answer:
56 hours
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
Let
x -----> the number of hours
y ----> the amount earned in dollars
This problem represent a proportional relationship between the variable x and the variable y
Find the value of the constant of proportionality k
[tex]k=y/x[/tex]
For (3,27) ----> [tex]k=27/3=9\ \$/h[/tex]
For (9,81) ----> [tex]k=81/9=9\ \$/h[/tex]
For (21,189) ----> [tex]k=189/21=9\ \$/h[/tex]
The constant of proportionality k is 9
The linear equation is
[tex]y=9x[/tex]
For y=$500
substitute in the equation and solve for x
[tex]500=9x[/tex]
Divide by 9 both sides
[tex]x=56\ hours[/tex]
