a gardener is planting two types of trees:

type a is 2 feet tall and grows at a rate of 25 inches per year.

type b is 10 feet tall and grows at a rate of 9 inches per year.

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

It will take 1/2 of a year or 6 months for these trees to be the same height.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Type A is 2 feet tall and grows at a rate of 25 inches per year.

Type B is 10 feet tall and grows at a rate of 9 inches per year.

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

x = Number of years

Type A = 2 + 25x

Type B = 10 + 9x

Let's solve for x, using the following equation:

Type A =  Type B

2 + 25x = 10 + 9x

25x - 9x = 10 - 2

16x = 8

x = 8/16 = 1/2

It will take 1/2 of a year or 6 months for these trees to be the same height.

Let's prove it, this way:

2 + 25x = 10 + 9x

2 + 25 (1/2) = 10 + 9 (1/2)

2 + 25/2 = 10 + 9/2

29/2 = 29/2

14.5 = 14.5