Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 hours and earned $520. What is his normal hourly rate?
x = hourly rate
40x + 12x = 520
Solve for x
10
13
To find Angelo's normal hourly rate, we can follow these steps:
Step 1: Determine the number of hours he worked at his normal hourly rate.
Since Angelo worked 40 hours in a week, we subtract this from the total hours worked to find the number of hours he worked at his normal rate.
46 hours - 40 hours = 6 hours
Step 2: Determine the number of hours he worked at double time.
The remaining 6 hours are the hours he worked at double time.
Step 3: Determine Angelo's extra pay for working overtime.
Angelo is paid double time for each hour worked over 40 hours. Therefore, he receives double his normal hourly rate for the 6 additional hours.
Extra pay = 6 hours * 2 * Normal hourly rate
Step 4: Calculate Angelo's total pay.
Total pay = Normal pay + Extra pay
Since we know he earned $520 in total, we can set up the equation:
$520 = Normal pay + Extra pay
Step 5: Solve for the normal hourly rate.
Substitute the expression for extra pay from step 3 into the equation from step 4.
$520 = Normal pay + (6 hours * 2 * Normal hourly rate)
$520 = Normal pay + (12 * Normal hourly rate)
Simplifying the equation:
$520 = Normal pay + 12 * Normal hourly rate
$520 = Normal pay + 12N (where N represents the numerical value of the Normal hourly rate)
Step 6: Substitute the value of Normal pay with the product of 40 hours and the hourly rate.
Since Angelo worked 40 hours at his normal hourly rate, we can write:
Normal pay = 40 hours * Normal hourly rate
Normal pay = 40N
Substitute this value into the equation from step 5:
$520 = 40N + 12N
Simplifying the equation further:
$520 = 52N
Step 7: Solve for N.
Divide both sides of the equation by 52:
$520 / 52 = N
$10 = N
Therefore, Angelo's normal hourly rate is $10.