Question

A gardener is planting two types of trees: Type A is 10 feet tall and grows at a rate of 7 inches per year. Type B is 3 feet tall and grows at a rate of 19 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

7 years

Explanation:

First, create expressions to represent the problem:

`a(x) = 10(12) + 7x \\ b(x) = 3(12) + 19x`

Simplify:

`a(x) = 120 + 7x \\ b(x) = 36 + 19x`

Now make the expressions equal to each other and solve:

`120 + 7x = 36 + 19x \\ 84 = 12x \\ x = 7`

The answer is 7 years