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.
Since the paycheck varies directly with the number of hours worked, we can write the equation in the form of:
p = kt
where k is the constant of proportionality.
Given that the paycheck is $312.50 for 25 hours of work, we can substitute these values into the equation to solve for k:
312.50 = k * 25
Dividing both sides by 25, we get:
k = 312.50 / 25
k = 12.50
Therefore, the equation for the relationship between hours of work and pay is:
p = 12.50t