Question

Logan genetically engineered a new type of fir tree and a new type of pine tree. The combined height of one fir tree and one pine tree is 212121 meters. The height of 444 fir trees stacked on top of each other is 242424 meters taller than one pine tree. How tall are the types of trees that Logan genetically engineered

Answer 1

Answer:

The types of trees that Logan genetically engineered are fir trees 9 meters tall and pine trees 12 meters tall.

Step-by-step explanation:

Given:

The combined height of one fir tree and one pine tree is 21 meters.

The height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree.

Now, to find the height of types of trees that Logan genetically engineered.

Let the height of fir tree be $x.$

And let the height of pine tree be $y.$

So, the combined height of both the trees:

$x+y=21\\\\x=21-y\ \ \ .....(1)$

As given, the height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree.

Thus,

$4x=y+24$

Now, substituting the value of $x$ from equation (1):

$4(21-y)=y+24$

$84-4y=y+24$

Subtracting both sides by 24 we get:

$60-4y=y$

Adding both sides by $4y$ we get:

$60=5y$

Dividing both sides by 5 we get:

$12=y\\\\y=12\ meters.$

The height of pine trees = 12 meters.

Now, substituting the value of $y$ in equation to get the height of fir trees:

$x=21-y\\\\x=21-12\\\\x=9\ meters.$

The height of fir trees = 9 meters.

Therefore, the types of trees that Logan genetically engineered are fir trees 9 meters tall and pine trees 12 meters tall.