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 equation that can be used to find the number of years it will take for the populations of the two animals to be equal is:
200 - 15n = 150 - 5n
To solve the equation, we can begin by simplifying it:
200 - 15n = 150 - 5n
-15n + 5n = 150 - 200
-10n = -50
n = (-50)/(-10)
n = 5
Therefore, it will take 5 years for the population of moose and mountain goats to be equal.
To complete the equation and solve it, we need to plug in the values for the decrease in population each year for both the moose and the mountain goats.
The equation is:
200 - 15n = 150 - 5n
Now, let's solve it:
-15n + 5n = 150 - 200
-10n = -50
n = 5
Therefore, it will take 5 years for the population of moose and mountain goats to be equal.
Let's break down the problem into an equation.
Four times the sum of a number and four can be expressed as: 4(x + 4)
Two multiplied by two less than three times the number can be expressed as: 2(3x - 2)
According to the given information, these two expressions are equal:
4(x + 4) = 2(3x - 2)
Now let's solve for x:
4x + 16 = 6x - 4
4x - 6x = -4 - 16
-2x = -20
Dividing both sides by -2:
x = -20 / -2
x = 10
Therefore, the solution to the problem is x = 10.
When using the most efficient method to solve the equation 2(x + 3) = 5x - 2, the first step to be performed is 1 for Distributive Property.
In order to rewrite the equation a = 10b - 7 in terms of b, Arthur should first add 7 to both sides of the equation.
After subtracting 8 from both sides of the equation 5y = 20x + 8, Tilda should divide both sides of the equation by 20 in order to rewrite the equation in terms of x.
Let's denote the length of the shorter section as x inches.
According to the given information, the longer section is 5 inches longer than the shorter section, which means its length is x + 5 inches.
Twice the length of the longer section is three times the length of the shorter section can be expressed as:
2(x + 5) = 3x
Now, we can solve this equation to find the length of the shorter section:
2x + 10 = 3x
Subtracting 2x from both sides:
10 = x
Therefore, the length of the shorter section is 10 inches.
200−
n=150−
n
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)
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