Chapter 9.8, Problem 56SR

To determine

To evaluate: the system of equations to represent their growth, to find and interpret the solution in the context of the situation.

Answer to Problem 56SR

This $x=12$ represents that after 12 years both the plant will have equal height.

Explanation of Solution

Given:

A blue spruce grows an average of 6 inches per year. A hemlock grows an average of 4 inches per year. A blue spruce is 4 feet tall and a hemlock is 6 feet tall.

Let ‘ x’ represents the number of years the plant lives.

Then according to the context of the situation,

The blue spruce grows, $y=4+\frac{1}{2}x$ , (6 inches means $\frac{1}{2}$ feet)

Then

The hemlock grows, $y=6+\frac{1}{3}x$ ,(4 inches means $\frac{1}{3}$ feet)

After solving the above two equation,

  $x=12$

This $x=12$ represents that after 12 years both the plant will have equal height.