Mathematics

Question

A gardener is planting two types of trees: Type A is 10 feet tall and grows at a rate of 10 inches per year. Type B is 6 feet tall and grows at a rate of 16 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

1 Answer

  • Answer:

    8

    Step-by-step explanation:

    Firstly, we want to convert all values to inches, (1 ft = 12 inches)

    So,

    Type A is 120 inches tall and Type B is 72 inches tall.

    Now,

    Type A grows at 10 inches per year and Type B grows at 16 inches per year.

    Let x be the number of years passed,

    so the height of Type A plants will be [tex]120 + 10x[/tex] after x years have passed.

    Similarly, Type B plants will be [tex]72 + 16x[/tex] after x years.

    Now, we can equate the two equations to find x.

    [tex]120 +10x=72 +16x[/tex]

    [tex]6x = 48[/tex]

    [tex]x=8[/tex]

    Therefore, the number of years it will take for these trees to be the same height is 8.

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