1. 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.

Question

a. Use the Distributive Property to rewrite the bear population in Year 3 without needing to use parentheses.

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

a. Using the Distributive Property, we can rewrite the bear population in Year 3 as 2x + 20 bears.

b. Let the number of bears in Year 1 be represented as x.
In Year 2, the population is x + 10 bears.
Given that the total number of bears in Year 2 is 42, we can write the equation:
x + 10 = 42
Subtract 10 from both sides to isolate x:
x = 32
Therefore, there were 32 bears in the park during Year 1.