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.
200 - n = 150 - n
To solve the equation, we need to isolate the variable.
200 - 150 = -n + n
50 = 0
Since the equation is inconsistent, there is no solution and the populations of moose and mountain goats will never be equal.
200−__n=150−__n
To complete the equation, we need to fill in the missing numbers for the decrease in population each year.
200 - 15n = 150 - 5n
To solve the equation, we need to isolate the variable.
200 - 150 = -5n + 15n
50 = 10n
Divide both sides of the equation by 10.
n = 5
It will take 5 years for the population 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?
Let's break down the problem and translate it into an equation.
Four times the sum of a number and four: 4(x + 4)
Two multiplied by two less than three times the number: 2(3x - 2)
So, the equation becomes: 4(x + 4) = 2(3x - 2)
Let's solve the equation:
4x + 16 = 6x - 4 (distribute on both sides)
16 = 2x - 4 (subtract 4x from both sides)
20 = 2x (add 4 to both sides)
x = 10
So, 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
The most efficient method to solve the equation 2(x+3) = 5x - 2 is to first distribute the 2 to the terms inside the parentheses.
So, the step performed first is the Distributive Property (1).
2(x+3)=5x−2
To solve the equation 2(x+3) = 5x - 2, the most efficient method is to first distribute the 2 to the terms inside the parentheses using the Distributive Property.
2(x+3) = 5x - 2
2 * x + 2 * 3 = 5x - 2
2x + 6 = 5x - 2
So, the step performed first is the Distributive Property (1).