Pete worked 7 hours and charged 390. Rosalee worked 8 hours and charged 430. If​ Pete's charge is a linear function of the number of hours​ worked, find the formula for​ Pete's rate, and how much he would charge for working 1010 hours for Fred?

First step is to rule out the useless information given, which is how much Rosalee charges. Next let's calculate the linear function for how much Pete charges.

In Pete's case:

Simplify:

To find the formula for Pete's rate, we need to determine the rate at which he charges per hour. We can set up a linear equation using the information provided:

Let ( h ) be the number of hours Pete worked, and let ( C ) be the charge.

Given: When ( h = 7 ), ( C = 390 ) When ( h = 8 ), ( C = 430 )

Using the point-slope formula ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ), where ( m ) is the slope (rate) and ( (x_1, y_1) ) and ( (x_2, y_2) ) are two points on the line:

( m = \frac{{430 - 390}}{{8 - 7}} = \frac{{40}}{{1}} = 40 )

So, Pete's rate is $40 per hour.

Now, to find out how much Pete would charge for working 10 hours, we can use the formula ( C = mh ), where ( m ) is the rate and ( h ) is the number of hours:

( C = 40 \times 10 = 400 )

Therefore, Pete would charge $400 for working 10 hours for Fred.