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 n be the number of years.
The equation for the moose population is:
200 - 15n
The equation for the mountain goat population is:
150 - 5n
To find the number of years it will take for the populations to be equal, we set the two equations equal to each other and solve for n:
200 - 15n = 150 - 5n
Subtract 150 from both sides:
200 - 150 - 15n = -5n
50 - 15n = -5n
Add 5n to both sides:
50 - 15n + 5n = -5n + 5n
50 - 10n = 0
Subtract 50 from both sides:
50 - 50 - 10n = 0 - 50
-10n = -50
Divide both sides by -10:
-10n / -10 = -50 / -10
n = 5
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 the number be x.
Four times the sum of a number and four can be represented as: 4(x + 4)
Two multiplied by two less than three times the number can be represented as: 2(3x - 2)
According to the problem, these two expressions are equal. So, we can set up the equation:
4(x + 4) = 2(3x - 2)
Simplifying the equation:
4x + 16 = 6x - 4
Subtracting 4x and adding 4 to both sides:
16 = 2x - 4
Adding 4 to both sides:
20 = 2x
Dividing both sides by 2:
x = 10
The solution to the problem is x = 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