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?
$\square

Explanation:

Step1: Calculate total hours worked

First, sum up all 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

Straight - time is 8 hours per day. For a week, regular hours (if we consider daily 8 - hour basis, but here we can also calculate total regular hours as \(8\times6 = 48\) hours (since there are 6 working days: M, Tu, W, Th, F, St). Wait, actually, let's check the hours:

Wait, the days are M (7.1), Tu (7.3), W (8.6), Th (9.1), F (10.7), St (10.1). So 6 days.

First, for each day, regular hours are 8, overtime is hours over 8.

Let's calculate overtime for each day:

- M: \(7.1\leq8\), overtime = 0
- Tu: \(7.3\leq8\), overtime = 0
- W: \(8.6 - 8=0.6\)
- Th: \(9.1 - 8 = 1.1\)
- F: \(10.7 - 8=2.7\)
- St: \(10.1 - 8 = 2.1\)

Now, total regular hours: \(7.1+7.3 + 8+8+8+8\)? Wait no, better to calculate total hours first: \(7.1 + 7.3+8.6 + 9.1+10.7+10.1=52.9\) hours.

Total regular hours: sum of minimum(8, hours per day) for each day.

M: 7.1, Tu:7.3, W:8, Th:8, F:8, St:8.

Sum of regular hours: \(7.1 + 7.3+8 + 8+8+8=46.4\) hours. Wait, no, that's wrong. Wait, actually, regular hours are 8 hours per day, so for days with hours ≤8, regular hours are the hours worked, for days >8, regular hours are 8.

So:

M: 7.1 (regular), 0 (overtime)

Tu:7.3 (regular), 0 (overtime)

W:8 (regular), 0.6 (overtime)

Th:8 (regular), 1.1 (overtime)

F:8 (regular), 2.7 (overtime)

St:8 (regular), 2.1 (overtime)

Now, total regular hours: \(7.1 + 7.3+8 + 8+8+8=46.4\) hours.

Total overtime hours: \(0.6 + 1.1+2.7+2.1 = 6.5\) hours.

Now, regular pay rate: \(\$8.60\) per hour.

Overtime pay rate: \(8.60\times1.5=\$12.90\) per hour.

Now, calculate regular pay: \(46.4\times8.60\)

Calculate overtime pay: \(6.5\times12.90\)

First, regular pay: \(46.4\times8.60\)

\(46.4\times8 = 371.2\), \(46.4\times0.6 = 27.84\), so \(371.2+27.84 = 399.04\)

Overtime pay: \(6.5\times12.90\)

\(6\times12.90 = 77.4\), \(0.5\times12.90 = 6.45\), so \(77.4 + 6.45=83.85\)

Total gross pay: \(399.04+83.85 = 482.89\)? Wait, no, maybe my regular hours calculation is wrong.

Wait, another approach: total hours worked: \(7.1 + 7.3+8.6 + 9.1+10.7+10.1 = 52.9\) hours.

Regular hours: 8 hours per day for 6 days: \(8\times6 = 48\) hours.

Overtime hours: \(52.9 - 48=4.9\) hours. Wait, that's different. Wait, why? Because when we calculate regular hours as 8 per day, total regular is \(8\times6 = 48\), regardless of how many hours are worked per day (as long as some days have less than 8, but the company's straight - time is based on 8 hours a day. Wait, the problem says "Straight - time is based on 8 hours a day with overtime at time - and - a - half". So straight - time pay is for 8 hours a day, and any hours over 8 in a day are overtime. But also, if a day has less than 8, does the straight - time still count as 8? Wait, no, probably, straight - time is the actual hours worked up to 8, and overtime is hours over 8. Wait, the problem says "Straight - time is based on 8 hours a day" – maybe it means that the regular rate is for 8 hours per day, and any hours worked beyond 8 in a day are overtime. So for a day with \(h\) hours, if \(h\leq8\), pay is \(h\times\) regular rate; if \(h > 8\), pay is \(8\times\) regular rate \(+(h - 8)\times\) overtime rate.

So let's recalculate:

- M: \(7.1\times8.60\)
- Tu: \(7.3\times8.60\)
- W: \(8\times8.60+0.6\times8.60\times1.5\)
- Th: \(8\times8.60 + 1.1\times8.60\times1.5\)
- F: \(8\times8.60+2.7\times8.60\times1.5\)
- St: \(8\times8.60+2.1\times8.60\times1.5\)

Now calculate each day's pay:

- M: \(7.1\times8.60 = 61.06\)
- Tu: \(7.3\times8.60=62.78\)
- W: \(8\times8.60+0.6\times8.60\times1.5=68.8+0.6\times12.9 = 68.8 + 7.74=76.54\)
- Th: \(8\times8.60+1.1\times12.9=68.8+14.19 = 82.99\)
- F: \(8\times8.60+2.7\times12.9=68.8 + 34.83=103.63\)
- St: \(8\times8.60+2.1\times12.9=68.8+27.09 = 95.89\)

Now sum all these:

\(61.06+62.78 = 123.84\)

\(123.84+76.54 = 200.38\)

\(200.38+82.99 = 283.37\)

\(283.37+103.63 = 387\)

\(387+95.89 = 482.89\)

Wait, but let's check the total hours again: \(7.1 + 7.3+8.6+9.1+10.7+10.1=52.9\) hours.

Regular rate: \(8.60\), overtime rate: \(8.60\times1.5 = 12.90\)

Regular hours: let's see, how many hours are at regular rate? The hours up to 8 per day. So for M:7.1, Tu:7.3, W:8, Th:8, F:8, St:8. So total regular hours: \(7.1 + 7.3+8+8+8+8=46.4\) hours. Overtime hours: \(52.9 - 46.4 = 6.5\) hours.

Regular pay: \(46.4\times8.60 = 46.4\times8+46.4\times0.6=371.2 + 27.84 = 399.04\)

Overtime pay: \(6.5\times12.90 = 83.85\)

Total: \(399.04+83.85 = 482.89\). So that's consistent.

Wait, but maybe the company considers the workweek as 40 hours? Wait, the problem says "straight - time is based on 8 hours a day", so 8*5 = 40? Wait, no, the days are M, Tu, W, Th, F, St – 6 days. So 8*6 = 48 hours. So the initial calculation is correct.

So the gross pay is \(\$482.89\)? Wait, let's recalculate the 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. Correct.

Regular hours: 8 hours per day for 6 days: 48 hours. Overtime: 52.9 - 48 = 4.9? Wait, no, that's a mistake! Oh no! I see the error. The days: M, Tu, W, Th, F, St – that's 6 days. But 8 hours per day for 6 days is 48 hours. But when we calculate the hours per day:

M:7.1 (<=8), Tu:7.3 (<=8), W:8.6 (>8), Th:9.1 (>8), F:10.7 (>8), St:10.1 (>8). So the hours at regular rate are:

M:7.1, Tu:7.3, W:8, Th:8, F:8, St:8. So total regular hours:7.1 + 7.3+8+8+8+8 = 46.4. Then overtime hours: (8.6 - 8)+(9.1 - 8)+(10.7 - 8)+(10.1 - 8)=0.6+1.1+2.7+2.1 = 6.5. Then total hours:46.4+6.5 = 52.9. Correct. So 46.4 regular, 6.5 overtime.

Regular pay:46.4*8.60 = 46.4*8 + 46.4*0.6 = 371.2+27.84 = 399.04

Overtime pay:6.5*12.90 = 83.85

Total:399.04+83.85 = 482.89. So that's the gross pay.

Answer:

\(482.89\)