Linear equations

Question

A gardener is planting two types of trees: 

Type A is 5 feet tall and grows at a rate of 14 inches per year.

Type B is 9 feet tall and grows at a rate of 6 inches per year.

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

Answer 1

First let's start by making an algebraic expression for each of the types of trees.

Type A is 5 feet tall and grows at a rate of 14 inches per year.

A = 5 + 14y

Type B is 9 feet tall and grows at a rate of 6 inches per year.

B = 9 + 6y

Now we just need to set them equal to each other and solve for y to find out how many years it will take for them to be the same height.

5 + 14y = 9 + 6y --> get y to one side by itself, let's move 6y to the left by subtracting from both sides.

5 + 8y = 9 --> let's move 5 to the right by subtracting it from both sides.

8y = 4 --> divide each side by 8

y = 1/2 --> Tree A and tree B will be the same height in half a year, or 6 months.