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.

Answer 1

8

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
`120 + 10x` after x years have passed.

Similarly, Type B plants will be
`72 + 16x` after x years.

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

`120 +10x=72 +16x`

`6x = 48`

`x=8`

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