Given:
a.) Type A is 9 feet tall and grows at a rate of 7 inches per year.
b.) Type B is 7 feet tall and grows at a rate of 11 inches per year.
First, for us to be able to determine how many years it will take for these trees to be the same height, let's generate the equation that represents the growth rate of each tree.
Let x = the number of years
(In inches)
For Type A: (9 x 12) + 7x = 108 + 7x
For Type B: (7 x 12) + 11x = 84 + 11x
Determining the how many years it will take for these trees to be the same height, the equation must be:
[tex]\text{ Height of Type A = Heigth of Type B}[/tex][tex]\text{ 108 + 7x = 84 + 11x}[/tex]Let's find x,
[tex]\text{ 108 + 7x = 84 + 11x}[/tex][tex]\text{ 7x - 11x = 84 - 108}[/tex][tex]\text{ -4x = -24}[/tex][tex]\frac{-4x}{-4}\text{ =}\frac{-24}{-4}[/tex][tex]\text{ x = 6 years}[/tex]Therefore, the trees will be of the same height in 6 years.