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.

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 solve the problem, let's first use the information given:

1. In Year 1, the number of bears is \( x \).
2. In Year 2, the population is \( x + 10 \).
3. The total number of bears in Year 2 is given as 42.

We can set up the equation based on the information provided for Year 2:

\[ x + 10 = 42 \]

Now, we can solve for \( x \):

1. Subtract 10 from both sides of the equation:

\[ x = 42 - 10 \]

2. Calculate the right side:

\[ x = 32 \]

So, the number of bears in the park during Year 1 is \( 32 \).

Explanation of the Answer

In summary, Roger determined in Year 1 that there were \( 32 \) bears in the park. The population increased to \( 32 + 10 = 42 \) bears in Year 2, which aligns with the given information that the total number of bears during Year 2 is 42. This solution verifies the data provided and demonstrates how the bear population increased over the two years, confirming that the initial population in Year 1 was indeed \( 32 \) bears.