Question

A gardener is planting two types of trees:

Type A is 7 feet tall and grows at a rate of 8 inches per year.
Type B is 9 feet tall and grows at a rate of 6 inches per year.

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

Answer 1

After 1 year, both the tress will be of the same height.

Explanation:

Let us assume in x years, both trees have same height.

Type A is 7 feet tall and grows at a rate of 8 inches per year.

⇒The growth of tree A in x years = x times ( Height growth each year)

= 8 (x) = 8 x

⇒Actual height of tree A in x years = Initial Height + Growth in x years

= 7 + 8 x

or, the height of tree A after x years = 7 + 8x

Type B is 9 feet tall and grows at a rate of 6 inches per year.

⇒The growth of tree B in x years = x times ( Height growth each year)

= 6 (x) = 6 x

⇒Actual height of tree B in x years = Initial Height + Growth in x years

= 9 + 6 x

or, the height of tree B after x years = 9 + 6x

According to the question:

After x years, Height of tree A =Height of tree B

⇒7 + 8x = 9 + 6x

or, 8x - 6x = 9 - 7

or, 2 x = 2

or, x = 2/2 = 1 ⇒ x = 1

Hence, after 1 year, both the tress will be of the same height.