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.
The linear equation can be completed as:
200 - 15n = 150 - 5n
To solve the equation, we can start by simplifying it:
200 - 150 = -5n + 15n
50 = 10n
Dividing both sides by 10:
50/10 = n
n = 5
Therefore, it will take 5 years for the population of moose and mountain goats to be equal.
To complete the linear equation, we need to identify the rates at which the populations are decreasing.
The population of moose is decreasing by 15 moose each year, so the rate of decrease is -15.
The population of mountain goats is decreasing by 5 mountain goats each year, so the rate of decrease is -5.
Now we can complete the equation:
200 - 15n = 150 - 5n
To solve the equation, we need to isolate the variable n. Let's start by combining like terms:
-15n + 5n = 150 - 200
-10n = -50
Next, we can solve for n by dividing both sides of the equation by -10:
n = (-50) / (-10)
n = 5
Therefore, it will take 5 years for the population of moose and mountain goats to be equal.