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The amount of a person’s paycheck, p, varies directly with the number of hours worked, t. For 25 hours of work, the paycheck is...Question
The amount of a person’s paycheck, p, varies directly with the number of hours worked, t. For 25 hours of work, the paycheck is $312.50. Write an equation for the relationship between hours of work and pay. Explain how you got your equation.
Answers
GPT-4o mini
Since the paycheck, \( p \), varies directly with the number of hours worked, \( t \), we can express this relationship with the equation:
\[
p = kt
\]
where \( k \) is the constant of proportionality.
To find the value of \( k \), we can use the information given in the problem. We know that for 25 hours of work, the paycheck is $312.50. Substituting these values into the equation gives:
\[
312.50 = k \times 25
\]
Now, we can solve for \( k \):
\[
k = \frac{312.50}{25} = 12.50
\]
Now that we have found \( k \), we can substitute it back into the original equation to get the final equation that relates hours worked to pay:
\[
p = 12.50t
\]
This equation means that for every hour worked, the person earns $12.50. This is how we derived the equation for the relationship between hours worked and pay.
\[
p = kt
\]
where \( k \) is the constant of proportionality.
To find the value of \( k \), we can use the information given in the problem. We know that for 25 hours of work, the paycheck is $312.50. Substituting these values into the equation gives:
\[
312.50 = k \times 25
\]
Now, we can solve for \( k \):
\[
k = \frac{312.50}{25} = 12.50
\]
Now that we have found \( k \), we can substitute it back into the original equation to get the final equation that relates hours worked to pay:
\[
p = 12.50t
\]
This equation means that for every hour worked, the person earns $12.50. This is how we derived the equation for the relationship between hours worked and pay.