Question

When Alexander moved into a new house, he planted two trees in his backyard. At

the time of planting, Tree A was 36 inches tall and Tree B was 21 inches tall. Each

year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per

year. Let A represent the height of Tree At years after being planted and let B

represent the height of Tree Bt years after being planted. Write an equation for each

situation, in terms of t, and determine which tree is taller after 3 years.

Answer 1

The equations for each situation are

A = 36 + 6t

B = 21 + 9t

After 3 years, Tree A is taller.

Explanation:

From the question,

Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and

Tree A grew by 6 inches per year and Tree B grew by 9 inches per year after planting.

For Tree A,

Given a period of t years after planting, the height would have increased by 6t

∴ A = 36 + 6t

For Tree B,

Given a period of t years after planting, the height would have increased by 9t

∴ B = 21 + 9t

To determine, which tree is taller after 3 years,

t = 3

For Tree A

A = 36 + 6t

A = 36 + 6(3)

A = 36 + 18

A = 54 inches

For Tree B

B = 21 + 9t

B = 21 + 9(3)

B = 21 + 27

B = 48 inches

Hence, After 3 years, Tree A is taller.