Question

The combined height of one oak tree and one pine tree is 21 meters. The height of 4 oak trees stacked on top of each other is 24 meters taller than one pine tree. How tall is the oak tree and the pine tree

Answer 1

Height of an oak tree= 9 meters

Height of a pine tree = 12 meters

Explanation:

Given:

The combined height of 1 oak tree and 1 pine tree = 21 meters

Height of 4 oak trees = 24 meters more than 1 pine tree

To find the height of 1 pine tree and height of one oak tree.

Solution:

Let the height of one oak tree be =
`x` meters.

Let height of one pine tree =
`y` meters.

Combined height can be given as :

`x+y=21`-------------[1]

Height of 4 oak trees = 24 meters more than 1 pine tree

The above statement can be given as :

`4x=24+y`------------[2]

Rearranging equation [2] by subtracting both sides by
`y`.

`4x-y=24+y-y`

`4x-y=24`-------------[2]

Adding rearranged equation [2] to [1].

`x+y=21`

`4x-y=24`

+--------------------

`5x\ = 45`

Dividing both sides by 5.

`(5x)/(5)=(45)/(5)`

∴
`x=9`

Plugging in
`x=9` in equation [1]

`9+y=21`

Subtracting both sides by 9.

`9-9+y=21-9\\\therefore y=12`

Height of an oak tree= 9 meters

Height of a pine tree = 12 meters