Question

Linear Equations in Real-World Scenarios Practice
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Question
The population of moose in a forest is 200, and it is decreasing by 15 moose each year. In the same forest, there are 150 mountain goats. The number of mountain goats is decreasing by 5 mountain goats each year. Let n
be the number of years. Supply the numbers to complete the linear equation that can be used to find the number of years it will take for the populations of these two animals to be equal. Then, solve the equation.(2 points)
200−
n=150−
n

It will take
years for the population of moose and mountain goats to be equal.

Remaining Attempts : 3
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Answer 1

To set up the linear equation based on the information provided, we will first express the populations of moose and mountain goats in terms of the number of years, \( n \).

1. **Population of Moose**: The initial population is 200, and it is decreasing by 15 moose each year. So, after \( n \) years, the population of moose can be expressed as:
\[
200 - 15n
\]

2. **Population of Mountain Goats**: The initial population is 150, and it is decreasing by 5 mountain goats each year. Therefore, after \( n \) years, the population of mountain goats can be expressed as:
\[
150 - 5n
\]

Now, we can set these two expressions equal to each other to find the point in time when the populations will be the same:
\[
200 - 15n = 150 - 5n
\]

Next, we will solve this equation for \( n \).

### Step 1: Move all terms involving \( n \) to one side
Add \( 15n \) to both sides:
\[
200 = 150 - 5n + 15n
\]
\[
200 = 150 + 10n
\]

### Step 2: Move constant terms to the other side
Subtract 150 from both sides:
\[
200 - 150 = 10n
\]
\[
50 = 10n
\]

### Step 3: Divide both sides by 10
\[
n = \frac{50}{10} = 5
\]

So, it will take **5 years** for the populations of moose and mountain goats to be equal.