A gardener is planting two types of trees: Type A is 3 feet tall and grows at a rate of 22 inches per year. Type B is 4 feet tall and grows at a rate of 20 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

  6 years

Step-by-step explanation:

The height of tree A can be modeled by ...

  A = 36 +22y . . . . . where y is the number of years, height is inches

The height of tree B can be modeled by ...

  B = 48 +20y . . . . . same deal

The two heights are the same when ...

  A = B

  36 +22y = 48 +20y

  2y = 12 . . . . . . subtract 36+20y

  y = 12/2 = 6

It will take 6 years for the trees to be the same height.

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Note that you can "cut to the chase" by recognizing that the taller tree is growing at the slower rate, so the 12-inch difference in height is being reduced by 2 inches per year. (That is the meaning of 2y=12, above.) From there, it is a simple step to get to the divide 12 by 2.

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58