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? each fir tree is meters tall and each pine tree is meters tall.

Explanation:

Step1: Set up equations

Let the height of a fir tree be \(x\) meters and the height of a pine tree be \(y\) meters.
We have the system of equations:
\(

$$\begin{cases}x + y=21\\4x=y + 24\end{cases}$$

\)

Step2: Substitute \(y\) from the first equation into the second equation

From \(x + y=21\), we get \(y = 21 - x\).
Substitute \(y = 21 - x\) into \(4x=y + 24\):
\(4x=(21 - x)+24\)
\(4x=21 - x+24\)
\(4x+x=21 + 24\)
\(5x=45\)
\(x = 9\)

Step3: Find \(y\)

Substitute \(x = 9\) into \(x + y=21\):
\(9+y=21\)
\(y=21 - 9\)
\(y = 12\)

Answer:

Each fir tree is \(9\) meters tall and each pine tree is \(12\) meters tall.