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.
The linear equation can be completed as follows:
200 - 15n = 150 - 5n
To solve this equation, we first simplify it:
-15n + 5n = 150 - 200
-10n = -50
Next, we divide both sides of the equation by -10:
n = (-50)/(-10)
n = 5
So, it will take 5 years for the population of moose and mountain goats to be equal.
The linear equation to find the number of years it will take for the populations of moose and mountain goats to be equal is:
200 - 15n = 150 - 5n
Now, let's solve the equation:
200 - 15n = 150 - 5n
To solve for n, we can simplify the equation by combining like terms:
-15n + 5n = 150 - 200
-10n = -50
Now, divide both sides of the equation by -10 to isolate n:
n = (-50) / (-10)
n = 5
Therefore, it will take 5 years for the population of moose and mountain goats to be equal.