1. Roger is a wildlife researcher who has been hired to study and track the

Question

population of bears in a national park. In Year 1 of the study, Roger determines
that the park is home to x bears. In Year 2, the population has increased to
x+10 bears, and in Year 3, the population has increased to 2(x+10) bears.b. The total number of bears in the park during Year 2 is 42. Write and solve a
linear equation to determine how many bears were in the park during Year
1. Explain the answer.

Answer 1

To determine the number of bears in the park during Year 1, we can start by using the information provided and formulating a linear equation.

1. Define the variables:

   • Let \( x \) be the number of bears in Year 1.

2. Year 2 population:

   • According to the problem, in Year 2, the population increases by 10 bears, so the number of bears in Year 2 is: \[ x + 10 \]

3. Given data for Year 2:

   • We know that the total number of bears in Year 2 is 42. Therefore, we can set up the following equation: \[ x + 10 = 42 \]

4. Solve the equation:

   • To find \( x \), we can isolate it on one side of the equation: \[ x = 42 - 10 \] \[ x = 32 \]

5. Conclusion:

   • This means that the number of bears in the park during Year 1 was 32.

Explanation of the Answer:

In Year 1, the initial bear population was determined to be 32 bears. Over the following year (Year 2), the population increased by 10, leading to a total of 42 bears, which was consistent with the information given. This indicates that Roger's analysis correctly reflects the growth in the bear population in the park during the years he studied. Thus, the population of bears can be tracked and analyzed effectively following these patterns.