Question

A gardener plants two types of trees in a park:

Type A is five feet tall and grows at a rate of 12 inches per year.
Type B is three feet tall and grows at a rate of 15 inches per year.

Algebraically determine how many years it will take for these trees to be the same height.

Answer 1

it will take 8 years for the trees to be the same height

Explanation:

Answer 2

8 years

Explanation:

Lets write an equation for Type A

The initial value is 5 ft and the slope 12 inches

We need to have the same units, so lets change 5 ft to inches

5 ft * 12 inches / ft = 60 inches

y = mx+b

y = 12 x + 60

Lets write an equation for Type B

The initial value is 3 ft and the slope 15 inches

We need to have the same units, so lets change 3 ft to inches

3 ft * 12 inches / ft = 36 inches

y = mx+b

y = 15 x + 36

We want to know when y is the same value. We can set the equations equal.

12x + 60 = 15x+36

Subtract 12 x from each side

12x-12x+60 = 15x-12x +36

60 =3x+36

Subtract 36 from each side

60-36 = 3x+36-36

24 = 3x

Divide each side by 3

24/3 = 3x/3

8 =x

It will take 8 years for the trees to be the same height