Roger is a wildlife researcher who has been hired to study and track the
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.
a. Use the Distributive Property to rewrite the bear population in Year 3
without needing to use parentheses.
2(x + 10) = 2x + 20
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.
Let the number of bears in Year 1 be x.
In Year 1: x bears
In Year 2: x + 10 bears
In Year 3: 2(x + 10) bears
Given that the total number of bears in Year 2 is 42, we can set up the equation:
x + 10 = 42
Solving for x:
x = 42 - 10
x = 32
Therefore, there were 32 bears in the park during Year 1.
Explanation: We know that the population of bears increased by 10 from Year 1 to Year 2. So, if we add this increase to the number of bears in Year 1, we should get the total number of bears in Year 2, which is 42. Hence, we solve for x using the equation x + 10 = 42 to determine that there were 32 bears in the park during Year 1.