It will take exactly 3 years for these trees to be the same height
Step-by-step explanation:
A gardener is planting two types of trees
- Type A is 9 feet tall and grows at a rate of 6 inches per year.
- Type B is 6 feet tall and grows at a rate of 18 inches per year.
We need to find exactly how many years it will take for these trees to be the same height
To solve this problem let us make an equation of each type and then equate the two equations to find the number of years
Assume that the two types will have the same heights in x years
∵ Type A is 9 feet tall and grows at a rate of 6 inches per year
- Change the feet to inches
∵ 1 foot = 12 inches
∴ 9 feet = 9 × 12 = 108 inches
The height of the tree after x years is the sum of the initial height and the product of the rate of growth and the number of years
∵ The rate of growth = 6 inches per year
∵ The number of years = x
∵ The initial height = 108 inches
∴ The height of tree A = 108 + 6 x
∵ Type B is 6 feet tall and grows at a rate of 18 inches per year
∵ 1 foot = 12 inches
∴ 6 feet = 6 × 12 = 72 inches
∵ The rate of growth = 18 inches per year
∵ The number of years = x
∵ The initial height = 72 inches
∴ The height of tree B = 72 + 18 x
Now equate the two equations to find x
∵ 72 + 18 x = 108 + 6 x
- Subtract 72 from both sides
∴ 18 x = 36 + 6 x
- Subtract 6 x from both sides
∴ 12 x = 36
- Divide both sides by 12
∴ x = 3
It will take exactly 3 years for these trees to be the same height
Learn more:
You can learn more about the linear equations in brainly.com/question/9801816
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