Question

A gardener is planting two types of trees:

Type A is 3 feet tall and grows at a rate of 12 inches per year.

Type B is 7 feet tall and grows at a rate of 4 inches per year.

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

Answer 1

6 years

Explanation:

Convert feet to inches: 3 feet = 36 inches, 7 feet = 84 inches

Set two equations equal to each other:

First equation, Type A has a slope of 12 (grows 12 inches per year) and a y-intercept of 36 (it starts 36 inches (or 3 feet) tall)

Second equation, Type B has a slope of 4 (grows 4 inches per year) and a y-intercept of 84 (starts at 84 inches (or 7 feet) tall)

12x + 36 = 4x + 84

subtract 36 from both sides

12x = 4x + 48

subtract 4x from both sides

8x = 48

divide by 8 on both sides

x = 6

It will take the tree types 6 years to be the same height

Hope that helps!