Question

A gardener is planting two types of trees:

Type A is 5 feet tall and grows at a rate of 13inches per year.

Type B is 3 feet tall and grows at a rate of 21 inches per year.

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

Answer 1

Answer: it will take 0.25 years for these trees to be the same height.

Explanation:

Let x represent the number of years that it will take these trees to be the same height.

Type A tree is 5 feet tall and grows at a rate of 13 inches per year. This means that the total height of Type A tree after x years would be

13x + 5

Type B tree is 3 feet tall and grows at a rate of 21 inches per year. This means that the total height of Type B tree after x years would be

21x + 3

For both trees to be of the same height, the number of years would be

13x + 5 = 21x + 3

21x - 13x = 5 - 3

8x = 2

x = 2/8 = 0.25