Answer: After 2 hours period, Grayson charges more than Ian.
Step-by-step explanation:
Let h represents the number of hours of tax preparation.
Given : Grayson charges $35 per hour plus a $35 administration fee for tax preparation.
Ian charges $45 per hour plus a $15 administration fee.
Also, Total charges = Admiration fee + rate per hour × (number of hours of tax preparation)
⇒ Expression for charges done by Grayson:-
![G(h)=35+35h](https://tex.z-dn.net/?f=G%28h%29%3D35%2B35h)
Expression for charges done by Ian:-
![I(h)=15+45h](https://tex.z-dn.net/?f=I%28h%29%3D15%2B45h)
Required equation :-
![G(h)>I(h)\\\\ 35+35h>15+45h](https://tex.z-dn.net/?f=G%28h%29%3EI%28h%29%5C%5C%5C%5C%2035%2B35h%3E15%2B45h)
Subtract 15 and 35 h from both sides , we get
![20>10h](https://tex.z-dn.net/?f=20%3E10h)
Divide both sides by 10, we get
![2>h](https://tex.z-dn.net/?f=2%3Eh)
⇒ Any hours greater than 2 , Grayson charges more than Ian.
⇒ After 2 hours period, Grayson charges more than Ian.