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# Business Math: Which is the better method for calculating overtime?

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(1)

Sally worked 48 hours this week . Her overtime rate is 1.5 times the regular rate. When calculating gross pay with overtime, there are two options:

Option 1. ( total regular hours X hourly rate ) + ( overtime hours X overtime rate ) = gross pay
OR
Option 2. ( total number of hours worked X the hourly rate) + ( hours over 40 X 0.5 the hourly rate ).

Most businesses prefer to use the first method to calculate gross pay. Discuss the reasons for this preference.

NOTE: You must show, with algebraic examples, that the two methods give you the same answer for the gross pay. Assume Sally worked 48 hours and her overtime rate is 1.5 times the regular pay, choose a regular rate to be anything you like ( for example 12 dollars an hour, etc) and use both methods to calculate the gross pay.

Explain why Method 1 is better than Method 2.

(2)

Most people think that if an increase in earnings moves their salary to a higher tax bracket , their entire salary will be taxed at the higher rate. Is this true? Give an example to justify your answer.

NOTE: You must explain to us how tax brackets work, using specific algebraic examples. Take a look at the tutorial attached to this. You must give your own, unique example. Explain it in your own words.

#### Solution Preview

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Sally worked 48 hours this week . Her overtime rate is 1.5 times the regular rate. When calculating gross pay with overtime, there are two options:

Option 1. ( total regular hours X hourly rate ) + ( overtime hours X overtime rate ) = gross pay, OR

Option2. ( total number of hours worked X the hourly rate) + ( hours over 40 X 0.5 the hourly rate ).
Most businesses prefer to use the first method to calculate gross pay. Discuss the reasons for this preference.

NOTE: You must show , with algebraic examples, that the two methods give you the same answer for the gross pay. Assume Sally worked 48 hours and her overtime rate is 1.5 times the regular pay , choose a regular rate to be anything you like ( for example 12 dollars an hour, etc) and use both methods to calculate the gross pay.

Explain why Method 1 is better than Method 2.

Option 1: Let the hourly rate be x. The total pay is

40x + 8(1.5x) = 40x + 12x = 52x

Option 2: The total pay is

48x + 8(0.5x) = 48x + 4x = 52x

Plug any hourly rate in for x, and you'll get the same total pay.

I think method 1 is better than method 2 because you're separating the regular number of hours worked from the number of overtime hours worked. In any ...

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