Question

A gardener is planting two types of trees: Type A is 6 feet tall and grows at a rate of 18 inches per year. Type B is 3 feet tall and grows at a rate of 21 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

1 year.

Explanation:
First set up the equation for each tree

Tree A = 6 + 18x

Tree B = 3 + 21x

Since we want to find how long it would take the tree to be same height just set the equation equal to each other.

6+18x = 3+21x

Now you can just solve it by isolating x.

First, subtract 18x from both sides so that we can have just one x and coefficient.

6 = 3 + 3x

Then, subtract 3 from both sides to isolate the x.

3 = 3x

Next, divide both sides by 3.

1 = x

X means the years and so that means it would take just 1 year for the trees to be same height.