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

Question

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 find the number of years \( n \) until the populations of moose and mountain goats are equal, you can set up the following linear equation based on the information provided:

Starting with the population of moose:

• The initial population of moose = 200
• The population decreases by 15 moose each year, so after \( n \) years, the population of moose will be:
  \( 200 - 15n \)

Now for the population of mountain goats:

• The initial population of mountain goats = 150
• The population decreases by 5 mountain goats each year, so after \( n \) years, the population of mountain goats will be:
  \( 150 - 5n \)

We want to find \( n \) when these two populations are equal:

\[ 200 - 15n = 150 - 5n \]

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

1. First, simplify the equation: \[ 200 - 15n = 150 - 5n \]

2. Add \( 15n \) to both sides: \[ 200 = 150 + 10n \]

3. Subtract 150 from both sides: \[ 50 = 10n \]

4. Divide both sides by 10: \[ n = 5 \]

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