A gardener is planting two types of trees: ● Type A: Starts at 4.5 feet tall and grows 8 inches per year. ● Type B: Starts at 2 feet tall and grows 10 inches per year. Write an equation to represent the year, y, when the trees will be the same height.

Answer 1

Let's denote the height of Type A trees after y years as A(y) and the height of Type B trees after y years as B(y).

The formula for the height of Type A trees after y years is:
A(y) = 4.5 + 8y

The formula for the height of Type B trees after y years is:
B(y) = 2 + 10y

To find the year when the trees will be the same height, we need to solve the equation A(y) = B(y):
4.5 + 8y = 2 + 10y

Now, we can solve this equation to find the value of y. Subtracting 4.5 from both sides:
8y = -2 + 10y

Subtracting 10y from both sides:
-2y = -2

Dividing both sides by -2:
y = 1

Therefore, the two types of trees will be the same height after 1 year.