The LCM and gcf of three number are respectively 360 and 3 if two number are 18 and 24 find third number
5=2x+y=x-y solve equation
To solve the equation 5 = 2x + y = x - y, we can rearrange it as follows:
2x + y = 5 (Equation 1)
x - y = 5 (Equation 2)
We can solve this system of equations using the method of elimination.
First, let's multiply Equation 2 by 2 to make the coefficients of x in both equations the same:
2(x - y) = 2(5)
2x - 2y = 10 (Equation 3)
Now, we can add Equation 1 and Equation 3 together:
(2x + y) + (2x - 2y) = 5 + 10
4x - y = 15 (Equation 4)
Next, let's add Equation 2 and Equation 4 together:
(x - y) + (4x - y) = 5 + 15
5x - 2y = 20 (Equation 5)
Now, let's solve Equation 5 for x:
5x - 2y = 20
5x = 2y + 20
x = (2y + 20) / 5
Finally, we substitute this value of x back into Equation 2:
x - y = 5
(2y + 20) / 5 - y = 5
2y + 20 - 5y = 25
-3y + 20 = 25
-3y = 5
y = -5/3
Therefore, the solution to the equation system is x = (2y + 20) / 5 and y = -5/3.
To find the third number, we need to use the relationship between the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of the numbers.
Given:
LCM of three numbers = 360
GCF of three numbers = 3
Let's assume the third number as x.
We know that:
LCM * GCF = Product of the three numbers
So, we can write the equation as:
360 * 3 = 18 * 24 * x
1080 = 432x
To find x, divide both sides of the equation by 432:
x = 1080 / 432
x = 2.5
Therefore, the third number is 2.5.
To find the third number, we need to use the relationship between the LCM and GCF.
We know that the LCM of three numbers is 360, so the product of the three numbers is equal to 360.
Let's assume that the third number is x.
So, we have:
18 * 24 * x = 360
Simplifying this equation, we get:
432x = 360
Dividing both sides of the equation by 432, we find:
x = 360 / 432
Simplifying further, we get:
x = 5 / 6
Therefore, the third number is 5/6 or 0.8333.