A gardener is planting two types of trees: Type A is 3 feet tall and grows at the rate of 13 inches per year. Type B is 10 feet tall and grows at a rate of 6 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Solution:

Let "x" be the number of years

Type A is 3 feet tall and grows at the rate of 13 inches per year

1 feet = 12 inches

3 feet = 3 x 12 = 36 inches

Equation: 36 + 13x eqn 1

Type B is 10 feet tall and grows at a rate of 6 inches per year

10 feet = 120 inches

Equation: 120 + 6x eqn 2

For both trees to be of same height, eqn 1 must be equal to eqn 2

36 + 13x = 120 + 6x

13x - 6x = 120 - 36

7x = 84

x = 12

Thus it takes 12 years for both trees to be of same height

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