It will take 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 6 feet tall and grows at a rate of 12 inches per year
Type B is 2 feet tall and grows at a rate of 24 inches per year
We need to find exactly 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
Type A:
∵ The initial height of the tree is 6 feet
∵ 1 foot = 12 inches
∴ 6 feet = 6 × 12 = 72 inches
∴ The initial height of the tree is 72 inches
∵ It grows at a rate of 12 inches per year
∵ The number of years is x
∴ The height of the tree in x years = 72 + 12 x
Type B:
∵ The initial height of the tree is 2 feet
∴ 2 feet = 2 × 12 = 24 inches
∴ The initial height of the tree is 24 inches
∵ It grows at a rate of 24 inches per year
∵ The number of years is x
∴ The height of the tree in x years = 24 + 24 x
Equate The heights of the two types
∴ 72 + 12 x = 24 + 24 x
- Subtract 2 from both sides
∴ 48 + 12 x = 24 x
- Subtract 12 x from both sides
∴ 48 = 12 x
- Divide both sides by 12
∴ x = 4
It will take 4 years for these trees to be the same height
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