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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.
MUST SHOW ALL WORK WILL MARK BRAINLEST TO WHOEVER ANSWERS CORRECTLY

Respuesta :

xKelvin

Answer:

A)

[tex]y=10.25x[/tex]

B)

24 hours

C)

$410

Step-by-step explanation:

We are given that Kelly’s paycheck varies directly with the number of hours she works.

We know that she received $133.25 for 13 hours of work.

Part A)

The standard form for the direct variation equation is:

[tex]y=kx[/tex]

Where k is the constant of variation.

Here, y is the paycheck amount and x is the number of hours Kelly worked.

We know that Kelly received $133.25 for 13 hours of work. Hence, y = 133.25 when x = 13:

[tex]133.25=13k[/tex]

Solve for k:

[tex]k=10.25\\[/tex]

Therefore, our constant of variation is 10.25.

We can substitute this into our equation:

[tex]y=10.25x[/tex]

Therefore, our direct variation equation is:

[tex]y=10.25x[/tex]

Contextually, the equation tells us that Kelly earns $10.25 per hour.

Part B)

Using the equation, we can determine the the number of hours Kelly worked to earn $246. We can substitute 246 for y:

[tex]246=10.25x[/tex]

Solve for x:

[tex]\displaystyle x=\frac{246}{10.25}=24[/tex]

Therefore, x = 24.

Therefore, Kelly must’ve worked 24 hours for her paycheck to be $246.

Part C)

We can use our equation. This time, we will substitute 40 for x and evaluate. Hence:

[tex]y=10.25(40)=\$410[/tex]

So, Kelly will earn $410 for working 40 hours.

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