Question

Mark worked 5 2/3, 9 1/3, 8 3/5, 9 2/5, and 9 hours during the week. If he earns $6.55 per hour, how much did he earn before deductions? (This may involve overtime.)

$312.99

$281.65

$201.84

$288.12

Answer 1

The answer is $281.65

5 2/3 = 5 + 2/3 = 15/3 + 2/3 = 17/3
9 1/3 = 9 + 1/3 = 27/3 + 1/3 = 28/3

8 3/5 = 8 + 3/5 = 40/5 + 3/5 = 43/5
9 2/5 = 9 + 2/5 = 45/5 + 2/5 = 47/5

The total number of hours is:
5 2/3 + 9 1/3 + 8 3/5 + 9 2/5 + 9 =
17/3 + 28/3 + 43/5 + 47/5 + 9 =
45/3 + 90/5 + 9 =
15 + 18 + 9 =
42

The hours of overtime are: 42 - 40 = 2
So, he earns $6.55 per hour for each 40 hours:
40h * 6.55$/h = $262

Overtime price is:
1 1/2 * $6.55 = (1 + 1/2) * $6.55 = (2/2 + 1/2) * $6.55 = 3/2 * $6.55 = $9.825 per hour

Two hours are overtime, so for those two hours he earned:
2h * 9.825$/h = $19.65

The total earn for 42 hours is:
$262 + $19.65 = $281.65