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.
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.
Answers
GPT-4o mini
To find the value of \( z \), we start by setting up the equation according to the information given.
From the problem, we know:
- 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 statement, the number of wolves in Year 2 is equal to the number of wolves in Year 3. Therefore, we can set up the equation:
\[
7 + z = 3z - 3
\]
Now, we will solve for \( z \).
1. First, we will subtract \( z \) from both sides:
\[
7 = 3z - z - 3
\]
This simplifies to:
\[
7 = 2z - 3
\]
2. Next, we will add 3 to both sides:
\[
7 + 3 = 2z
\]
This simplifies to:
\[
10 = 2z
\]
3. Finally, divide both sides by 2:
\[
z = 5
\]
Thus, the value of \( z \) is \( 5 \).
### Conclusion:
The number of wolves in Year 1 (z) is 5.
From the problem, we know:
- 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 statement, the number of wolves in Year 2 is equal to the number of wolves in Year 3. Therefore, we can set up the equation:
\[
7 + z = 3z - 3
\]
Now, we will solve for \( z \).
1. First, we will subtract \( z \) from both sides:
\[
7 = 3z - z - 3
\]
This simplifies to:
\[
7 = 2z - 3
\]
2. Next, we will add 3 to both sides:
\[
7 + 3 = 2z
\]
This simplifies to:
\[
10 = 2z
\]
3. Finally, divide both sides by 2:
\[
z = 5
\]
Thus, the value of \( z \) is \( 5 \).
### Conclusion:
The number of wolves in Year 1 (z) is 5.