3) The amount of Kelly’s paycheck varies directly with the number of hours she works. Kelly receives $133.25 for 13 hours of work. (a) Write a direct variation equation that relates the amount of Kelly’s paycheck, p, to the number of hours, h, Kelly works.
(b) Use the equation to find the number of hours Kelly works when her paycheck is $246.
(c) Use the equation to find the amount of Kelly’s paycheck when she works 40 hours.

a. Direct variation equation is: p = 10.25h

b. Number of hours Kelly work is 24 when her paycheck is $246

c. Kelly's paycheck is $410 when she works 40 hours

Step-by-step explanation:

Direct variation means that the increase in one quantity causes increase in other.

Let p be the paycheck of Kelly and h be the number of hours then

p∝h

Removing the proportional symbol introduces a proportionality constant

    Eqn 1

Now we know, Kelly receives $133.25 for 13 hours of work.

Putting in equation 1

Putting the value of k in equation 1

     Eqn 2

a. Direct variation equation: p = 10.25h

b. Number of hours when paycheck is 246.

Putting this value in equation 2

c. Paycheck when she works 40 hours

Putting in equation 2

Hence,

a. Direct variation equation is: p = 10.25h

b. Number of hours Kelly work is 24 when her paycheck is $246

c. Kelly's paycheck is $410 when she works 40 hours

Answer is in image below