Question

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.

Answer 1

6 years

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 answer: divide 12 by 2.