Question

2. 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.

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

Answer 1

To find the value of \( z \), we can set up an equation based on the information provided:

1. In Year 1, the number of wolves is \( z \).
2. In Year 2, the number of wolves is \( 7 + z \).
3. 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. We can set up the equation:

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

Now, let’s solve this equation for \( z \):

1. First, get all terms involving \( z \) on one side. Subtract \( z \) from both sides:

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

This simplifies to:

\[
7 = 2z - 3
\]

2. Next, add 3 to both sides:

\[
7 + 3 = 2z
\]

So we have:

\[
10 = 2z
\]

3. Now, divide both sides by 2:

\[
z = \frac{10}{2} = 5
\]

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

### Verification:
- Year 1: \( z = 5 \)
- Year 2: \( 7 + z = 7 + 5 = 12 \)
- Year 3: \( 3z - 3 = 3(5) - 3 = 15 - 3 = 12 \)

Both Year 2 and Year 3 have 12 wolves, confirming that our solution is correct. Thus,

\[
\boxed{5}
\] is the value of \( z \).