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 21 meters. The height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree. How tall are the types of trees that Logan genetically engineered?

Answer 1

Given :

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

And

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

To Find :

The height of fir tree

The height of pine tree

Solution :

Let The height of fir tree = $F_h$  meter

Let The height of pine tree = $P_h$ meter

According to question

The height of fir tree + The height of pine tree = 21 m

i.e  $F_h$  + $P_h$  = 21          ...............1

Again

 4 × height of fir tree = 24 +  height of pine tree

i.e   4 $F_h$ = 24 + $P_h$

Or,   4 $F_h$ - $P_h$ = 24         ...........2

Solving eq 1 and eq 2

       ( 4 $F_h$ - $P_h$ ) + ( $F_h$ + $P_h$ ) = 24 + 21

or,     ( 4 $F_h$ + $F_h$ ) + ( - $P_h$ + $P_h$ ) = 45

Or,     5 $F_h$ + 0 = 45

∴                 $F_h$ = $\dfrac{45}{5}$

i.e               $F_h$ = 9

So,  The height of fir tree =  $F_h$ = 9 meters

And

Put the value of  $F_h$ into eq 1

∵  $F_h$  + $P_h$  = 21    

So, 9 +  $P_h$  = 21    

∴     $P_h$ = 21 - 9

i.e   $P_h$ = 12 meters

So,  The height of pine tree =  $P_h$ = 12 meters

Hence,  The height of fir tree that Logan genetically engineered is 9 meters .

And The height of pine tree that Logan genetically engineered is 12 meters

Answer

Answer 2

Answer:

Step-by-step explanation: