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)
Let's suppose that after n years, the population of moose will be equal to the population of mountain goats.
The equation for the population of moose after n years is given by:
Moose population = 200 - 15n
The equation for the population of mountain goats after n years is given by:
Mountain goat population = 150 - 5n
Setting these two equations equal to each other, we have:
200 - 15n = 150 - 5n
To solve this equation, let's first simplify it by combining like terms:
-15n + 5n = 150 - 200
This simplifies to:
-10n = -50
Next, let's isolate n by dividing both sides of the equation by -10:
n = (-50)/(-10)
This simplifies to:
n = 5
Therefore, it will take 5 years for the populations of moose and mountain goats to be equal.
Four times the sum of a number and four is the same as two multiplied by two less than three times the number. What is e solution to this problem? (1 point)
Let's denote the number as x.
According to the given equation, we have:
4(x + 4) = 2(3x - 2)
Let's simplify the equation step by step:
4x + 16 = 6x - 4
Next, let's isolate the variable by subtracting 6x from both sides of the equation:
16 = 2x - 4
Now, let's add 4 to both sides of the equation:
20 = 2x
Finally, let's divide both sides of the equation by 2 to solve for x:
x = 10
Therefore, the solution to the equation is x = 10.
Let's set up the linear equation to find the number of years it will take for the populations of moose and mountain goats to be equal.
Let n be the number of years.
The population of moose after n years can be expressed as 200 - 15n.
The population of mountain goats after n years can be expressed as 150 - 5n.
To find when the populations will be equal, we set the two expressions equal to each other:
200 - 15n = 150 - 5n
Simplifying the equation, we get:
-15n + 5n = 150 - 200
-10n = -50
Dividing both sides of the equation by -10:
n = (-50)/(-10)
n = 5
Therefore, it will take 5 years for the populations of moose and mountain goats to be equal.