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

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 $18x$ 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.