The amount of a person’s paycheck p varies directly with the number of hours worked t. For 16 hours of work, the paycheck is $124.00. Write an equation for the relationship between hours of work and pay.

Question

p = 77.50t

p = t + 7.75

p = t + 77.50

p = 7.75t

Answer 1

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.

Given that for 16 hours of work, the paycheck is $124.00, we can find the value of \( k \):

1. Substitute \( p = 124 \) and \( t = 16 \) into the direct variation equation: \[ 124 = k \cdot 16 \]

2. Solve for \( k \): \[ k = \frac{124}{16} = 7.75 \]

Now we can write the equation relating hours worked to paycheck: \[ p = 7.75t \]

Therefore, the correct equation is:

\[ \boxed{p = 7.75t} \]