Question

some companies use the overtime premium method to determine gross earnings. use this method to complete the following payroll ledger. overtime is paid at the time - and - a - half rate for all hours over 40. the regular gross earnings is the regular rate times the total hours. the overtime gross earnings is the overtime premium rate times the overtime hours.

name	s	m	t	w	th	f	s	total hrs.	reg. rate	o.t hrs.

gross earnings

name	regular	overtime premium	total

how many hours total did mr. vern work?
51 hours

how many overtime hours did mr. vern work?
□ hours

Explanation:

Part 1: Total Hours Worked

Step1: Sum daily hours

Add hours for each day: \( 8.4 + 8.2 + 8.4 + 8.5 + 8.1 + 9.4 \)

Step2: Calculate total

\( 8.4 + 8.2 = 16.6 \); \( 16.6 + 8.4 = 25 \); \( 25 + 8.5 = 33.5 \); \( 33.5 + 8.1 = 41.6 \); \( 41.6 + 9.4 = 51 \)

Step1: Identify regular hours

Regular hours threshold is 40.

Step2: Subtract from total

Overtime hours = Total hours - 40 = \( 51 - 40 = 11 \)

Step1: Recall formula

Regular earnings = Regular rate × Total hours (wait, no—regular earnings is regular rate × regular hours? Wait, problem says: "The regular gross earnings is the regular rate times the total hours." Wait, no, re-reading: "The regular gross earnings is the regular rate times the total hours. The overtime gross earnings is the overtime premium rate times the overtime hours." Wait, maybe typo, but as per problem: regular earnings = reg rate × total hours? Wait, no, maybe "regular hours" is 40? Wait, no, problem statement: "regular gross earnings is the regular rate times the total hours"—wait, that might be error, but let's check. Wait, regular rate is $7.42, total hours 51? No, that can't be. Wait, maybe "regular hours" is 40. Wait, no, problem says: "regular gross earnings is the regular rate times the total hours"—maybe misstatement. Wait, let's check the problem again: "The regular gross earnings is the regular rate times the total hours. The overtime gross earnings is the overtime premium rate times the overtime hours." Overtime premium rate is time-and-a-half, so overtime premium rate = \( 7.42 × 0.5 = 3.71 \) (since time-and-a-half is 1.5×, so premium is 0.5×). Wait, but first, regular earnings: if regular earnings is reg rate × total hours, that would be \( 7.42 × 51 \). But that seems high. Wait, maybe the problem has a mistake, but as per problem:

Step1: Calculate regular earnings

Regular earnings = \( 7.42 × 51 \)

Step2: Compute

\( 7.42 × 51 = 7.42 × (50 + 1) = 7.42×50 + 7.42×1 = 371 + 7.42 = 378.42 \)

Answer:

51 hours

Part 2: Overtime Hours Worked