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)
For the moose population, the linear equation can be written as:
200 - 15n
For the mountain goat population, the linear equation can be written as:
150 - 5n
To find the number of years when the populations of these two animals will be equal, we can set the two equations equal to each other:
200 - 15n = 150 - 5n
Simplifying the equation, we get:
10n = 50
Dividing both sides by 10, we find:
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 the solution to this problem?(1 point)
Let's assume the number is represented by n.
The equation can be written as:
4(n + 4) = 2(3n - 2)
Expanding both sides of the equation, we get:
4n + 16 = 6n - 4
Subtracting 4n from both sides and adding 4 to both sides, we have:
16 + 4 = 6n - 4n
20 = 2n
Dividing both sides by 2, we get:
n = 10
Therefore, the solution to the problem is n = 10.
When using the most efficient method to solve the following problem, what step is performed first? Enter 1 for Distributive Property or 2 for Subtraction Property of Equality.
2 (x+3) = 5x − 2
1. Distributive Property
Arthur writes the equation a=10b−7. He wants to rewrite it in terms of b. In Arthur’s first step, what value should he add to both sides of the equation?(1 point)
To find the number of years it will take for the populations of moose and mountain goats to be equal, we can set up a linear equation.
Let's assume after n years, the population of moose will be equal to the population of mountain goats.
The population of moose decreases by 15 each year, so after n years, the population of moose will be 200 - 15n.
The population of mountain goats decreases by 5 each year, so after n years, the population of mountain goats will be 150 - 5n.
Setting these two expressions equal, we can set up the equation:
200 - 15n = 150 - 5n
To solve for n, we can simplify the equation:
-15n + 5n = 150 - 200
-10n = -50
n = (-50)/(-10)
n = 5
So, it will take 5 years for the populations of moose and mountain goats to be equal.