Question

Type A is 2 feet tall and grows at a rate of 17 inches per year. Type B is 10 feet tall and grows at a rate of 5 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

Therefore after 3 years the height of these tree will be same.

Explanation:

Given that,

Type A is 2 feet tall and grows at a rate of 17 inches.

Type B is 10 feet tall and is growing at a rate of 5 inches.

1 feet = 12 inches,

2 feet= (12×2) inches = 24 inches

5 feet= (12×5) inches = 60 inches

Let after t years, the height of these tree will be same.

After t years, the height of type A is =(24+17t)

After t years, the height of type B is =(60+5t)

According to the problem,

24+17t=60+5t

⇒17t-5t=60-24

⇒12t = 36

⇒t =
`(36)/(12)`

⇒t=3

Therefore after 3 years the height of these tree will be same.