Agardener is planting two types of trees:

type a is 7 feet tall and grows at a rate of 8 inches per year.
type b is 9 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

After 1 year, both the tress will be of the same height.

Step-by-step explanation:

Let us assume in x years, both trees  have same height.

Type A  is 7 feet tall and grows at a rate of 8 inches per year.

⇒The growth of tree A in x years = x times  ( Height growth each year)

                                                        = 8 (x)  = 8 x

⇒Actual height of tree A in x years  = Initial Height + Growth in x years

                                                             = 7 + 8 x

or, the height of tree A after  x years  = 7 + 8x

Type B is 9 feet tall and grows at a rate of 6 inches per year.

⇒The growth of tree B in x years = x times  ( Height growth each year)

                                                        = 6 (x)  = 6 x

⇒Actual height of tree B in x years  = Initial Height + Growth in x years

                                                             = 9 + 6 x

or, the height of tree B after  x years  = 9 + 6x

According to the question:

After x years, Height of tree A  =Height of tree B

⇒7 + 8x   = 9 + 6x

or, 8x - 6x = 9 - 7

or, 2 x  = 2

or, x  =  2/2  = 1    ⇒ x  = 1

Hence, after 1 year, both the tress will be of the same height.

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step-by-step explanation: