Question

A gardener is planting two types of trees:

Answer 1

It will take exactly 4 years for these trees to be the same height

Step-by-step explanation:

A gardener is planting two types of trees:

• Type A is 3 feet tall and grows at a rate of 7 inches per year
• Type B is 5 feet tall and grows at a rate of 1 inches per year

We need to find in how many years it will take for these trees to be the

same height

Assume that it will take x years for these trees to be the same height

The height of a tree = initial height + rate of grow × number of years

Type A:

∵ The initial height = 3 feet

∵ 1 foot = 12 inches

∴ The initial height = 3 × 12 = 36 inches

∵ The rate of grows = 7 inches per year

∵ The number of year = x

∴ $h_{A}$ = 36 + (7) x

∴ $h_{A}$ = 36 + 7 x

Type B:

∵ The initial height = 5 feet

∴ The initial height = 5 × 12 = 60 inches

∵ The rate of grows = 1 inches per year

∵ The number of year = x

∴ $h_{B}$ = 60 + (1) x

∴ $h_{B}$ = 60 + x

Equate $h_{A}$ and $h_{B}$

∴ 36 + 7 x = 60 + x

- Subtract x from both sides

∴ 36 + 6 x = 60

- Subtract 36 from both sides

∴ 6 x = 24

- Divide both sides by 6

∴ x = 4

∴ The two trees will be in the same height in 4 years

It will take exactly 4 years for these trees to be the same height

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