Question

erin covery 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.

hours worked
employee\tsu\tm\ttu\tw\tth\tf\tst\twage
covery, e\t—\t7.9\t7.7\t8.6\t8.8\t10.9\t10.9\t$9.00

what is erins gross pay for the week?
$

Explanation:

Step 1: Calculate total hours worked

First, sum up all the hours worked each day: \(7.9 + 7.7 + 8.6 + 8.8 + 10.9 + 10.9\). Let's calculate that: \(7.9+7.7 = 15.6\); \(15.6+8.6 = 24.2\); \(24.2+8.8 = 33\); \(33 + 10.9 = 43.9\); \(43.9+10.9 = 54.8\) hours total.

Step 2: Determine straight - time and overtime hours

Straight - time is 8 hours per day. There are 5 working days (M, Tu, W, Th, F, St? Wait, Su is not worked. So days worked: M, Tu, W, Th, F, St – 6 days? Wait, no, the time card has Su as “—”, so she worked 6 days? Wait, no, let's check the hours. Wait, straight - time is 8 hours a day. So for each day, hours up to 8 are straight - time, over 8 are overtime.

Let's calculate straight - time hours: For each day, minimum of hours worked and 8, then sum.

• M: 7.9 (all straight - time, since 7.9 < 8)
• Tu: 7.7 (all straight - time)
• W: 8.6 (8 straight - time, 0.6 overtime)
• Th: 8.8 (8 straight - time, 0.8 overtime)
• F: 10.9 (8 straight - time, 2.9 overtime)
• St: 10.9 (8 straight - time, 2.9 overtime)

Straight - time hours: \(7.9+7.7 + 8+8+8+8\)
\(7.9 + 7.7=15.6\); \(8\times4 = 32\); total straight - time: \(15.6+32 = 47.6\)

Overtime hours: Total hours - straight - time hours. Total hours is 54.8, so overtime hours: \(54.8 - 47.6 = 7.2\)

Wait, alternatively, calculate overtime for each day:

• M: 7.9, no overtime (7.9 < 8)
• Tu: 7.7, no overtime
• W: 8.6 - 8 = 0.6 overtime
• Th: 8.8 - 8 = 0.8 overtime
• F: 10.9 - 8 = 2.9 overtime
• St: 10.9 - 8 = 2.9 overtime

Overtime hours: \(0.6 + 0.8+2.9 + 2.9=7.2\)

Straight - time hours: Total hours - overtime hours = \(54.8-7.2 = 47.6\)

Step 3: Calculate pay for straight - time and overtime

Straight - time pay rate: \(\$9.00\) per hour. Overtime pay rate: \(1.5\times9=\$13.50\) per hour.

Straight - time pay: \(47.6\times9\)
\(47.6\times9=(40\times9)+(7\times9)+(0.6\times9)=360 + 63+5.4 = 428.4\)

Overtime pay: \(7.2\times13.5\)
\(7.2\times13.5 = 7\times13.5+0.2\times13.5=94.5 + 2.7 = 97.2\)

Step 4: Calculate gross pay

Gross pay = straight - time pay+overtime pay = \(428.4+97.2 = 525.6\)

Wait, let's check the total hours again. Wait, maybe I made a mistake in the number of days. Wait, the time card: Su is not worked. So days: M, Tu, W, Th, F, St – 6 days. Let's recalculate total hours: 7.9 (M) + 7.7 (Tu)+8.6 (W)+8.8 (Th)+10.9 (F)+10.9 (St). Let's add again: 7.9 + 7.7 = 15.6; 15.6+8.6 = 24.2; 24.2+8.8 = 33; 33+10.9 = 43.9; 43.9+10.9 = 54.8. Correct.

Alternative approach: For each day, calculate straight time (up to 8) and overtime (over 8), then sum pay for each day.

• M: 7.9 hours, pay: \(7.9\times9 = 71.1\)
• Tu: 7.7 hours, pay: \(7.7\times9 = 69.3\)
• W: 8 hours straight, 0.6 overtime. Pay: \(8\times9+0.6\times13.5=72 + 8.1 = 80.1\)
• Th: 8 hours straight, 0.8 overtime. Pay: \(8\times9+0.8\times13.5=72 + 10.8 = 82.8\)
• F: 8 hours straight, 2.9 overtime. Pay: \(8\times9+2.9\times13.5=72+39.15 = 111.15\)
• St: 8 hours straight, 2.9 overtime. Pay: \(8\times9+2.9\times13.5=72 + 39.15 = 111.15\)

Now sum these daily pays: \(71.1+69.3 = 140.4\); \(140.4+80.1 = 220.5\); \(220.5+82.8 = 303.3\); \(303.3+111.15 = 414.45\); \(414.45+111.15 = 525.6\)

Answer:

\(525.6\)