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

Answer 1

To complete the equation, we need to fill in the blanks correctly based on the information provided.

The equation represents the populations of moose and mountain goats over the years. Starting with the initial populations:

• The initial population of moose is 200, and it decreases by 15 moose each year, represented as \(200 - 15n\).
• The initial population of mountain goats is 150, and it decreases by 5 mountain goats each year, represented as \(150 - 5n\).

Now, we can write the linear equation to find the number of years \(n\) when both populations will be equal:

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

Now, let's solve the equation for \(n\).

1. Rearranging the equation: \[ 200 - 150 = 15n - 5n \] \[ 50 = 10n \]

2. Dividing both sides by 10: \[ n = \frac{50}{10} = 5 \]

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

To summarize:

• The completed equation is: \(200 - 15n = 150 - 5n\)
• It will take 5 years for the populations of moose and mountain goats to be equal.