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Question

Difficulty: MediumWages, Salaries, and Commissions

A machinist earns a regular hourly rate of $26.00\$26.00 for a standard 4040-hour workweek. Any hours worked over 4040 in a single week are paid at a time-and-a-half overtime rate. Additionally, working the night shift adds a flat $3.50\$3.50 per hour differential to their base rate before the overtime multiplier is applied. If the machinist worked 4646 hours last week, and all of those hours were on the night shift, what was their total gross pay in dollars?

Answer: 1445.5 $

Answer

1445.50
The total gross pay is calculated by first establishing the adjusted base rate for the night shift, which is the regular rate plus the differential: $26.00+$3.50=$29.50\$26.00 + \$3.50 = \$29.50. The machinist worked 4040 regular hours at this rate, earning 40×$29.50=$1,180.0040 \times \$29.50 = \$1,180.00. The 66 remaining hours are overtime, paid at 1.51.5 times the adjusted rate: $29.50×1.5=$44.25\$29.50 \times 1.5 = \$44.25. Multiplying this by the 66 overtime hours gives 6×$44.25=$265.506 \times \$44.25 = \$265.50. Adding the regular pay and overtime pay results in a total gross pay of $1,180.00+$265.50=$1,445.50\$1,180.00 + \$265.50 = \$1,445.50.

Step-by-Step Solution

1
Calculate the adjusted base hourly rate.
$26.00+$3.50=$29.50\$26.00 + \$3.50 = \$29.50 per hour
The night shift differential is added to the standard base rate before any other multipliers are applied.
2
Calculate the regular pay for the first 40 hours.
40×$29.50=$1,180.0040 \times \$29.50 = \$1,180.00
The standard workweek is 40 hours, which is paid at the regular adjusted rate.
3
Calculate the overtime hourly rate.
$29.50×1.5=$44.25\$29.50 \times 1.5 = \$44.25 per hour
Overtime is paid at time-and-a-half (1.5 times the regular rate), applying to the adjusted base rate.
4
Calculate the pay for the overtime hours.
6×$44.25=$265.506 \times \$44.25 = \$265.50
The machinist worked 46 hours total, so 6 of those hours are considered overtime.
5
Calculate the total gross pay.
$1,180.00+$265.50=$1,445.50\$1,180.00 + \$265.50 = \$1,445.50
Total gross pay is the sum of the regular shift pay and the overtime pay.

Key Concept

Calculating gross pay involving base rate adjustments, shift differentials, and overtime multipliers.
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Topics

Wages, Salaries, and Commissions

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