A gardener is planting two types of trees: Type A is 7 feet tall and grows at a rate of 2 inches per year. Type B is 2 feet tall and grows at a rate of 17 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer: it will take 0.33 years for the heights to be the same.

Step-by-step explanation:

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

Type A is 7 feet tall and grows at a rate of 2 inches per year. This means that the height of the tree after x years would be

2x + 7

Type B is 2 feet tall and grows at a rate of 17 inches per year. This means that the height of the tree after x years would be

17x + 2

For the heights to be the same, the number of years would be

17x + 2 = 2x + 7

17x - 2x = 7 - 2

15x = 5

x = 5/15

x = 0.33 years