By setting the height of the trees to variables, we can set up a system of equations. We’ll represent the height of the fir tree using the variable F, and the height of the pine using P. The height of one fir tree plus the height of one pine tree is 21 m, so we can set up an equation that looks like this.
F + P = 21
We also know that the height of four fir trees is equal to the height of a pine tree plus 24 m. Knowing this, we can set up an equation that looks like this.
4F = 24 + P
Next, we have to decide on a method to solve this system. The easiest method for this system is substitution. First, we will solve one of the equations so that one variable is by itself. I’ll choose the first one.
F + P = 21
We can subtract P from both sides, giving us
F = 21 - P
Now that we have one equation solved for F, we can substitute the F in the second equation with 21 - P, which we know is equal to F, allowing us to calculate the value of P. This gives us this equation.
4(21 - P) = 24 + P
First, we can distribute that four across the parentheses.
84 - 4P = 24 + P
We can then subtract P from both sides.
84 - 5P = 24
We can then subtract 84 from both sides
-5P = -60
Finally, we’ll divide by -5.
P = 12 m
Now that we know that the pine trees are 12 m tall, we can plug this value into either of our equations to calculate the height of the fir tree. I’ll choose the first equation.
F + 12 = 21
Here, all we need to do a subtract 12.
F = 9 m
The pine trees are 12 m tall, and the fir trees are 9 m tall.