Math problem about hours worked and wages earned. In a regular week, there are 5 working days and for each day, the working hours are 8.A man gets $ 2.40 per hour for regular work and $ 3.20 per hours for over-time. If he earns $ 432 in 4 weeks, then how many hours does he work for?

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Let the number of days worked be 'x' and the number of extra hours worked be 'y'

Thus, total hours worked = (8*x) + y...........(1)

Total amount gained = 2.4*(8*x) + (3.2*y) = 432............(2)

Now, there are 4 weeks and each week has 5 working days and each day with...

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Let the number of days worked be 'x' and the number of extra hours worked be 'y'

Thus, total hours worked = (8*x) + y...........(1)

Total amount gained = 2.4*(8*x) + (3.2*y) = 432............(2)

Now, there are 4 weeks and each week has 5 working days and each day with 8 regular working hours

Thus, total regular working hours in 4 weeks = 4*5*8 = 160 hours...........(3)

Using (3) in (2) we get

2.4*160 + (3.2*y) = 432

or, 384 + (3.2*y) = 432

or, 3.2*y = 48

or, y = 48/3.2 = 480/32 = 15

Thus, overtime hours = y = 15............(4)

Thus, total hours of working in 4 weeks = (3) + (4) = 160 + 15 = 175 hours.

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He works 160 hours of regular work and 15 hours of overtime.

Here's how to arrive at this answer.

He works 8 hours a day, 5 days a week for 4 weeks.  This means you multiply 8*5 and get 40 hours per week and multiply that by 4 and get 160.

160 hours times $2.40 per hour is $384.

So then you subtract $384 from $432 and you get $48.  That means he earned $48 of overtime.

You divide $48 by $3.20 and you get 15.

So that's 160 hours of regular work and 15 of overtime.

Approved by eNotes Editorial Team