Question

In part-time work, you receive 50 pesos per hour(h), if and only

if you work at most 25 hours per week. On the other hand, if you
go on overtime or if you work beyond 25 hours, your rate
becomes 1.25 times your regular hourly rate of 50 pesos.

A. Write a piecewise function that gives your total weekly pay P
in terms of the number of hours you worked or P(h). Note:
There should be two modes of weekly pay here. One, without
overtime and the other with overtime.
B. How much is your overtime pay if you worked for 40 hours?
C. How much will be your total weekly pay for clocking 40 hours
of work?(This means: Without overtime + With overtime pay) 8.

Answer 1

A. The piecewise function for total weekly pay is P(h) = { P1 = 50h, if h <= 25 and P2 = 1.25(50h - (25 * 50)) + (25 * 50), if h > 25}. B. The overtime pay for working 40 hours is 2187.5 pesos. C. The total weekly pay for working 40 hours is 4187.5 pesos.

Step-by-step explanation:

A. To write a piecewise function that gives the total weekly pay P in terms of the number of hours worked (h), we can define two modes of pay: one without overtime and the other with overtime pay. Let's call the regular pay without overtime P1 and the pay with overtime P2. The piecewise function can be written as:

P(h) = { P1 = 50h, if h <= 25
P2 = 1.25(50h - (25 * 50)) + (25 * 50), if h > 25}

B. To calculate the overtime pay if you worked for 40 hours, we need to find the difference between the total pay with overtime and the total pay without overtime. Using the piecewise function from part A, P(40) = P2 = 1.25(50 * 40 - (25 * 50)) + (25 * 50) = 1.25(2000 - 1250) + 1250 = 1.25(750) + 1250 = 937.5 + 1250 = 2187.5 pesos.

C. To calculate the total weekly pay for clocking 40 hours of work, we need to add the pay without overtime to the overtime pay. Using the piecewise function from part A, P(40) = P1 + P2 = 50 * 40 + 2187.5 = 2000 + 2187.5 = 4187.5 pesos.