Question

a business analyst makes 20$ an hour for the first 42 hours he works during a week and 28$ an hour for each worked over 42 hours. which piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week

Answer 1

y=(20 × 42) + [28 × (x-42)]

Answer 2

`y=28(x-42)+840`

Explanation:

Let he works for x hours in total.

We are given that he makes 20$ an hour for the first 42 hours

So, he earns in 1 hour = 20

He earns in 42 hours =
`20 *42`

=
`840`

Now we are given that he earns $28 an hour for each hour worked over 42 hours.

Since he worked for 42 hours out of x hours .

So, remaining hours = x-42 hours

So,he earns for x-42 hours =
`28*(x-42)`

y denotes his total earning of weekly

So, total earning
`y=28(x-42)+840`

Hence piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week is
`y=28(x-42)+840`