Question

Type A is 8 feet tall and grows at a rate of 18 inches per year. Type B is 9 feet tall and grows at a rate of 17 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

12 years.

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
`18x` 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
`96+18x` 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
`17x` inches and total height of type B would be
`108+17x` 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:

`96+18x=108+17x`

`96+18x-17x=108+17x-17x`

`96+x=108`

`96-96+x=108-96`

`x=12`

Therefore, after 12 years the height of these trees will be the same.