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

Let f be the height of the fir trees
Let p be the height of the pine trees

We know from the problem that
f + p = 21 and 4f = 24 + p
rearrange the 2nd equation to get p = 4f - 24 and substitute into the other equation

so...
f + 4f - 24 = 21
5f - 24 = 21
5f = 45
f = 9 - height of the fir tree

substitute back into the 1st equation
9 + p = 21
p = 12 - height of the pine tree