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

Answer:

Height of an oak tree= 9 meters

Height of a pine tree = 12 meters

Step-by-step 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.

$\frac{5x}{5}=\frac{45}{5}$

∴ $x=9$

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