The smith family and the jackson family are having their basements remodeled. the? smith's contractor charges? $16.50 per hour plus? $289 in supplies. the? jackson's contractor charges? $18.75 per hour and? $274.60 in supplies. at how many hours of work will the total cost be the same for both? families?

Answer  

Find out the At how many hours of work will the total cost be the same for both families .

To prove

Let us assume that the number of hours at which the total cost be the same for both families be x .

As given

Smith's family contractor charges $16.50 per hour plus $289 in supplies .

Jackson's family contractor charges $18.75 per hour and  $274.60 in supplies.

Than the equation becomes

16.50x + 289 = 18.75x + 274.60

16.50x -  18.75x = 274.60 - 289

-2.25x = -14.4

x = 6.4 hours

Therefore in 6.4 hours of work will the total cost be the same for both families .

third option: 6x+8

step-by-step explanation:

we can see that the given question is a sum of series and the values of n vary from 0 to 3

the first term will be:

when n=0, [(0)*x+2] => (0+2) => 2

when n=1, [(1)*x+2] => (x+2) => x+2

when n=2, [(2)*x+2] => 2x+2

when n=4, [(3)*x+2] => 3x+2

so adding up all the terms will give us:

=2+x+2+2x+2+3x+2

=x+2x+3x+2+2+2+2

=6x+8

so,

third option is the correct answer ..