The difference between two numbers is 108 less than their sum.If the larger number is twice the smaller number,find the difference between the two numbers.
x-y+108= x+y
x= 2y
2y-y+108 = 2y+y
Y+108= 3y
108= 2y
Y= 54
X= 108
2y-y+108=2y+y
y+108=3y
108=3y-y
108=2y
y=108/2
y=54
x=2y
x=2X54
x=108
To find the difference between the two numbers, let's assign variables.
Let's say the smaller number is x, and the larger number is y.
According to the problem, the difference between the two numbers (y - x) is 108 less than their sum (x + y), which can be expressed as:
y - x = (x + y) - 108
We are also given that the larger number (y) is twice the smaller number (x), so we can write:
y = 2x
Now, we can substitute the value of y from the second equation into the first equation:
2x - x = (x + 2x) - 108
x = 3x - 108
Multiplying both sides of the equation by -1, we get:
-x = -3x + 108
Adding 3x to both sides of the equation, we have:
2x = 108
Dividing both sides of the equation by 2, we get:
x = 54
Now that we have found the value of x, we can substitute it back into one of the equations to find the value of y:
y = 2x = 2 * 54 = 108
So, the larger number is 108 and the smaller number is 54.
The difference between the two numbers is:
y - x = 108 - 54 = 54
Therefore, the difference between the two numbers is 54.