Question

Jin is a wildlife researcher hired to track the population of wolves in the same
national park. In Year 1 of the study, there are z wolves; in Year 2 of the
study, there are 7+z wolves; and in Year 3 of the study, there are 3z-3 wolves.
The number of wolves in Year 2 is equal to the number of wolves in Year 3.

a. Write and solve a linear equation to determine the value of z.

Answer 1

To find the value of \( z \), we start by setting up the equation based on the information given.

In Year 1, the number of wolves is \( z \).
In Year 2, the number of wolves is \( 7 + z \).
In Year 3, the number of wolves is \( 3z - 3 \).

According to the problem, the number of wolves in Year 2 is equal to the number of wolves in Year 3:

\[
7 + z = 3z - 3
\]

Now, we'll solve for \( z \).

1. First, we can rearrange the equation to isolate \( z \) on one side. We'll start by subtracting \( z \) from both sides:

\[
7 = 3z - z - 3
\]

This simplifies to:

\[
7 = 2z - 3
\]

2. Next, add 3 to both sides to isolate the term with \( z \):

\[
7 + 3 = 2z
\]

This simplifies to:

\[
10 = 2z
\]

3. Finally, divide both sides by 2 to solve for \( z \):

\[
z = \frac{10}{2}
\]

Thus, we find:

\[
z = 5
\]

Therefore, the value of \( z \) is \( 5 \).