Question

A gardener is planting two types of trees take a is 4 feet tall and grows at a rate of 22 inches per year Tybee is 6 feet tall and grows at a rate of 18 inches per year algebraically determine exactly how many years you will take for these trees could be the same height

Answer 1

After 6 years both the trees will be of same height

Solution:

Let "x" be the number of years that both the trees take to be the same height

Type A is 4 feet tall and grows at a rate of 22 inches per year

We know that,

1 feet = 12 inches

4 feet = 4 x 12 inches = 48 inches

Therefore height of type A after x years is given as:

⇒ initial height + 22 inches per year

⇒ 48 + 22(x)

⇒ 48 + 22x ---- eqn 1

Type B is 6 feet tall and grows at a rate of 18 inches per year

We know that,

1 feet = 12 inches

6 feet = 12 x 6 inches = 72 inches

Therefore height of type B after x years is given as:

⇒ initial height + 18 inches per year

⇒ 72 + 18(x)

⇒ 72 + 18x ---- eqn 2

For height Type A to equal height Type B:

Height Type A = Height Type B

eqn 1 = eqn 2

48 + 22x = 72 + 18x

22x - 18x = 72 - 48

4x = 24

x = 6

Therefore after 6 years both the trees will be of same height