Algebraically determine exactly how many years it will take for these trees to be the same height

Question

A gardener is planting two types of trees: 

Type A is 10 feet tall and grows at a rate of 14 inches per year.

Type B is 8 feet tall and grows at a rate of 16 inches per year.

Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

Alright, so we want the trees to be the same height. We need to know how many years this will take.

Let the number of year passed be x. (If you have covered this in science you might know time as the independent variable).

Therefore tree A grows at a rate of 14x and tree B grows at a rate of 16x

Now we want the height to be equivalent so we have to also account for the starting height.

Type A's height after x years will be 10(12) +14x and Type B's height after x years will be 8(12) +16 x. We are multiplying the initial height in feet by 12 to get all the units in inches.

We know that both equations use x as the years passed. So, to find out when the height will be the same we can set both height expressions equal to each other.

10(12) +14x = 8(12)+16x

120+14x= 96 +16 x

Subtracting 96 from both sides : 24 +14x = 16x

Subtracting 14x from both sides : 24 + 2x

Therefore x= 12.

It will take 12 years for both tree types to be the same height. You can substitute x back in both expressions and confirm that the heights are equal.

Please let me know if you have more questions.