Question

erin moore works at the bubbles bath shoppe. she is an hourly worker. straight - time is based on 8 hours a day with overtime at time - and - a - half. calculate her gross pay based on her time card.
employee moore, e.
hours worked: su (—), m (7.1), tu (7.3), w (8.6), th (9.1), f (10.7), st (10.1)
wage: $8.80
what is erins gross pay for the week?

Explanation:

Step1: Calculate total hours worked

First, sum up the hours worked each day: \(7.1 + 7.3 + 8.6 + 9.1 + 10.7 + 10.1\)
\(7.1+7.3 = 14.4\); \(14.4 + 8.6 = 23\); \(23 + 9.1 = 32.1\); \(32.1 + 10.7 = 42.8\); \(42.8 + 10.1 = 52.9\) hours total.

Step2: Determine regular and overtime hours

Regular hours per week (8 hours/day × 6 days? Wait, no, days worked: M, Tu, W, Th, F, St → 6 days? Wait, straight - time is 8 hours a day. So regular hours: 8 hours/day × number of days worked. Number of days worked: 6 days (M, Tu, W, Th, F, St). So regular hours = \(8\times6 = 48\) hours. Overtime hours = total hours - regular hours = \(52.9 - 48 = 4.9\) hours.

Step3: Calculate regular pay

Regular pay rate is \(\$8.80\) per hour. Regular pay = regular hours × regular rate = \(48\times8.80=\$422.4\)

Step4: Calculate overtime pay

Overtime rate is time - and - a - half, so overtime rate = \(8.80\times1.5=\$13.2\) per hour. Overtime pay = overtime hours × overtime rate = \(4.9\times13.2=\$64.68\)

Step5: Calculate gross pay

Gross pay = regular pay + overtime pay = \(422.4+64.68=\$487.08\)

Wait, let's check the total hours again. Wait, maybe I made a mistake in the number of days. Let's recalculate total hours: \(7.1 + 7.3=14.4\); \(14.4 + 8.6 = 23\); \(23+9.1 = 32.1\); \(32.1+10.7 = 42.8\); \(42.8 + 10.1=52.9\). Now, regular hours: for each day, straight - time is 8 hours. So for each day, hours up to 8 are regular, over 8 are overtime.

Let's calculate regular and overtime per day:

- Monday: 7.1 hours (all regular, since 7.1 < 8)
- Tuesday: 7.3 hours (all regular, 7.3 < 8)
- Wednesday: 8.6 hours. Regular: 8, Overtime: \(8.6 - 8 = 0.6\)
- Thursday: 9.1 hours. Regular: 8, Overtime: \(9.1 - 8 = 1.1\)
- Friday: 10.7 hours. Regular: 8, Overtime: \(10.7 - 8 = 2.7\)
- Saturday: 10.1 hours. Regular: 8, Overtime: \(10.1 - 8 = 2.1\)

Now, total regular hours: \(7.1+7.3 + 8+8+8+8=7.1 + 7.3+40 = 14.4 + 40 = 54.4\)? Wait, no, that's wrong. Wait, no, the straight - time is based on 8 hours a day. So for each day, the first 8 hours are regular, anything over 8 is overtime.

So let's recalculate regular and overtime per day:

- Monday: 7.1 hours (regular: 7.1, overtime: 0)
- Tuesday: 7.3 hours (regular: 7.3, overtime: 0)
- Wednesday: 8.6 hours (regular: 8, overtime: 0.6)
- Thursday: 9.1 hours (regular: 8, overtime: 1.1)
- Friday: 10.7 hours (regular: 8, overtime: 2.7)
- Saturday: 10.1 hours (regular: 8, overtime: 2.1)

Now total regular hours: \(7.1+7.3 + 8+8+8+8=7.1 + 7.3+40 = 54.4\)? Wait, that can't be, because 7.1+7.3 = 14.4; 14.4+8+8+8+8=14.4 + 32 = 46.4 regular hours. Overtime hours: (8.6 - 8)+(9.1 - 8)+(10.7 - 8)+(10.1 - 8)=0.6 + 1.1+2.7 + 2.1 = 6.5 hours. Total hours: 46.4+6.5 = 52.9, which matches the total we calculated before.

Ah, I see my mistake earlier. The number of days with regular 8 hours: for Monday and Tuesday, the hours are less than 8, so all their hours are regular. For Wednesday, Thursday, Friday, Saturday, we take 8 hours as regular and the rest as overtime.

So regular hours: \(7.1+7.3 + 8+8+8+8=7.1 + 7.3+32 = 46.4\) hours.

Overtime hours: \((8.6 - 8)+(9.1 - 8)+(10.7 - 8)+(10.1 - 8)=0.6 + 1.1+2.7 + 2.1 = 6.5\) hours.

Regular pay: \(46.4\times8.80\)
\(46\times8.8 = 404.8\); \(0.4\times8.8 = 3.52\); so \(46.4\times8.8 = 404.8+3.52 = 408.32\)

Overtime rate: \(8.8\times1.5 = 13.2\) per hour.

Overtime pay: \(6.5\times13.2 = 85.8\)

Gross pay: \(408.32+85.8 = 494.12\)

Wait, let's recalculate \(46.4\times8.8\):

\(46.4\times8.8=(40 + 6 + 0.4)\times8.8=40\times8.8+6\times8.8 + 0.4\times8.8=352+52.8+3.52 = 352+56.32 = 408.32\)

\(6.5\times13.2 = 6\times13.2+0.5\times13.2 = 79.2+6.6 = 85.8\)

\(408.32+85.8 = 494.12\)

Yes, that's correct.

Answer:

\(\$494.12\)