Question

Michael recently started a new hourly wage job. The equation y=18.75x + 2500 models his total pay, y, in dollars as it relates to the number of hours, x, that he has worked.A. What is Miguel's hourly rate of pay?B. Does it appear the Miguel received a signing bonus? If so, how much was the bonus?How many hours must Miguel worked to receive $10,000 in total pay?

Answer 1

Given

y = 18.75x + 2500

Part A:

Based on the given equation where x is the number of hours worked. Since the coefficient of this term is 18.75, then we can conclude that Miguel's hourly rate is $18.75.

Part B:

The given equation has a constant of 2500, at x = 0, where the number of hours worked is zero, then the value of the equation is 2500. This appears that Miguel has a signing bonus, and the amount of bonus is $2500.

Part C:

Substitute y = 10000, to the equation and solve for x

$\begin{gathered} y=18.75x+2500 \\ 10000=18.75x+2500 \\ 10000-2500=18.75x \\ 7500=18.75x \\ 18.75x=7500 \\ \frac{18.75x}{18.75}=\frac{7500}{18.75} \\ x=400 \end{gathered}$

Therefore, Miguel must work 400 hours to receive $10,000 in total.