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21 December, 17:34

A tree that is 2 feet tall is growing at a rate of 1 foot per year.

A 6 foot tall tree is growing at a rate of ½ foot per year. In how

many years will the trees be the same height? How tall will the

trees be? system of equations

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Answers (1)
  1. 21 December, 20:02
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    H=2+1y, or h=2+y where h is the final height, 2 is the original height, and 1y, or y, is the rate of feet per year.

    h=6+1/2y, or h=6+0.5y, where h is the final height, 6 is the original height, and 1/2 y, or 0.5y, is the rate of feet per year.

    Now, we plug in heights to try and find a number of years that they will be the same height.

    Let's start with 12 feet.

    12=2+1y

    12=2+y

    12-2=y

    10=y

    12=6+0.5y

    12-6=0.5y

    6=0.5y

    12=y

    We seem to be fairly close, so we'll try something a little larger, 18 feet.

    18=2+y

    18-2=y

    16=y

    18=6+0.5y

    18-6=0.5y

    12=0.5y

    24=y

    This seems to be much farther away, so we'll try a smaller number, 10 feet.

    10=2+y

    10-2=y

    8=y

    10=6+0.5y

    10-6=0.5y

    4=0.5y

    8=y

    The years are the same now, so we know that in 8 years, the trees will be the same height. We also know that they both will be 10 feet height tall.
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