Answer:
12 years.
Step-by-step explanation:
Le x represent number of years.
We have been given that type A is 8 feet tall and grows at a rate of 18 inches per year. So growth of type A in x years would be [tex]18x[/tex] inches.
1 feet = 12 inches.
8 feet = 8*12 inches = 96 inches.
9 feet = 9*12 inches = 108 inches.
The total height of type A would be [tex]96+18x[/tex] inches.
We are also told that type B is 9 feet tall and grows at a rate of 17 inches per year. So growth of type B in x years would be [tex]17x[/tex] inches and total height of type B would be [tex]108+17x[/tex] inches.
To find the years when both trees will be of the same height, we will equate height of both trees and solve for x as:
[tex]96+18x=108+17x[/tex]
[tex]96+18x-17x=108+17x-17x[/tex]
[tex]96+x=108[/tex]
[tex]96-96+x=108-96[/tex]
[tex]x=12[/tex]
Therefore, after 12 years the height of these trees will be the same.
