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.
Let's start by translating the information given into equations:
In Year 1: z wolves
In Year 2: 7+z wolves
In Year 3: 3z-3 wolves
Since the number of wolves in Year 2 is equal to the number of wolves in Year 3, we can set up the following equation:
7+z = 3z-3
Now, we solve for z:
7+z = 3z-3
Add 3 to both sides:
10 + z = 3z
Subtract z from both sides:
10 = 2z
Divide by 2:
z = 5
Therefore, the value of z is 5.