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.
3
Algebraically determine how many years it will take for these trees to be the same hei
.
HINT: Turn feet to inches then equal to each

Answer 1

8 years

Explanation:

The hint does help a lot!

Convert the feet to inches: 5 feet = 60 inches, 3 feet = 36 inches

Make two equations: For Type A, the slope is 12 (grows 12 inches a year) and the y intercept is 60 (starts at 60 inches tall)

For Type B, the slope is 15 (grows 15 inches a year) and the y intercept is 36 (starts at 36 inches tall)

Set the two equations equal to each other, and solve for x:

12x + 60 = 15x + 36

subtract 36 from both sides

12x + 24 = 15x

subtract 12x from both sides

24 = 3x

divide both sides by 3

8 = x

It will take them 8 years to be the same height, and their height will be (12(8) + 60) or (15(8) + 36) = 156 inches