Question

A gardener is planting two types of trees:

Type A is 8 feet tall and grows at a rate of 16 inches per year.
Type B is 5 feet tall and grows at a rate of 20 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the
same height

Answer 1

9 years

Explanation:

The equation for Type A

Change the ft to inches

8ft *12 = 96 inches tall

96 + 16y

where y is the number of years

The equation for Type B

Change the ft to inches

5ft *12 = 60 inches tall

60 + 20y

where y is the number of years

Set the two equations equal to see when they will be the same height

96+16y = 60+20y

Subtract 16y from each side

96+16y-16y = 60+20y-16y

96 = 60+4y

Subtract 60 from each side

96-60 = 60-60+4y

36 = 4y

Divide each side by 4

36/4 = 4y/4

9 = y