Math question?

Question

If you are paid $12 an hour for up to 40 hours per week and a time and a half overtime, how many hours would you have to work in a week to earn $624?

My teacher told me to use this equation for it:

624 = 12(40) + 18(h-40)

My question is: Can someone explain to me WHY that equation came out of that word problem?

Step by step, please.

Answer 1

$12 is the amount you get paid times 40 hours per week
$12hr/2 = 6 so that $18 is time and a half times maximum hours you worked minus 40hrs.
so if you worked 48hrs
$12(40) + 18(48 - 40)
480 + 18(8) = 624

Answer 2

Let h = hours worked in a week

Equation:
$12(40) + ([$12 * 150%][h - 40]) = $624
$480 + ($18[h - 40]) = $624
$480 + $18h - $720 = $624
$18h = $864
h = 48

Answer: 48 hours

Explanation:
40 hours is maximum regular no. of hours per week; you are paid $12 per regular hours rendered.

Over and above 40 hours you are entitled to overtime. You are paid $12 plus 50% overtime premium such that your per hour rate is $18 for overtime.

So to plug:
= ($12 * 40 hrs) + ($18 * 8 hrs)
= $480 + $144
= $624 your total earnings for the week.

I hope this helps.

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Answer 3

624 is obviously your total from working
on the other side of the equation, the 12(40) represents him working for 40 hours at 12 dollars an hour.
the 18 in 18(h-40) comes from his overtime wage ($12/hour*1.5) and the (h-40) in it has the "-40" part of it to take into account the hours they've already worked (you could just leave that out and add 40 to whatever the h in 18(h) ended up being)
So basically, when you subtract the $480 that was given (12*40=480) from both sides and distribute the 18, you are left with
244=18h-720
(add 720 to both sides)
964=18h
h=53 5/9
meaning he worked almost 54 hours in the week, 40 of which he was paid normally for, and around 14 hours of overtime

Answer 4

h is the total number of hours worked.
time and a half means 1.5 X 12 = $18 an hour

So for the first 40 hours you get 12 x 40
then for each additional hours (h-40) you get 18 x (h-40)
total = 12x40 + 18x(h-40)
hence the eq above.