Question
The amount of a person’s paycheck p varies directly with the number of hours worked t. For 22 hours of work, the paycheck is $126.50. Write an equation for the relationship between hours of work and pay.
p = 5.75t
p = 57.50t
p = t + 57.50
p = t + 5.75
p = 5.75t
p = 57.50t
p = t + 57.50
p = t + 5.75
Answers
GPT-4o mini
Since the amount of a person's 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 \( k \), we can use the information that for 22 hours of work, the paycheck is $126.50:
\[
p = kt
\]
Substituting the known values:
\[
126.50 = k \cdot 22
\]
Now, solve for \( k \):
\[
k = \frac{126.50}{22} = 5.75
\]
Now that we have found \( k \), we can write the equation relating \( p \) and \( t \):
\[
p = 5.75t
\]
So, the correct option is:
**p = 5.75t**
To find \( k \), we can use the information that for 22 hours of work, the paycheck is $126.50:
\[
p = kt
\]
Substituting the known values:
\[
126.50 = k \cdot 22
\]
Now, solve for \( k \):
\[
k = \frac{126.50}{22} = 5.75
\]
Now that we have found \( k \), we can write the equation relating \( p \) and \( t \):
\[
p = 5.75t
\]
So, the correct option is:
**p = 5.75t**