The difference between two numbers is 18. If four times the smaller is less than three times the larger by 18, find the numbers.
y-x = 18
4x = 3y-18
Now finish it off.
Let's denote the smaller number as x and the larger number as y.
According to the given information, the difference between the two numbers is 18:
y - x = 18 ---(Equation 1)
It is also stated that four times the smaller number is less than three times the larger number by 18:
4x < 3y - 18 ---(Equation 2)
To find the values of x and y, we can solve these two equations simultaneously.
First, let's isolate y in Equation 1:
y = x + 18
Now, substitute this value of y in Equation 2:
4x < 3(x + 18) - 18
Simplify the equation:
4x < 3x + 54 - 18
4x - 3x < 54 - 18
x < 36
So, the smaller number x is less than 36.
Now, substitute the value of x in Equation 1 to find y:
y = x + 18
y = 36 + 18
y = 54
Therefore, the smaller number is x = 36 and the larger number is y = 54.
To solve this problem, let's assume that the smaller number is 'x', and the larger number is 'y'. We have two pieces of information:
1) The difference between the two numbers is 18:
y - x = 18 ...(equation 1)
2) Four times the smaller number is less than three times the larger number by 18:
4x < 3y - 18 ...(equation 2)
Now, let's solve these two equations simultaneously to find the values of x and y.
From equation 1, we can rewrite it as:
y = x + 18
Substituting this value of y into equation 2, we get:
4x < 3(x + 18) - 18
Expanding the equation gives:
4x < 3x + 54 - 18
Simplifying further:
4x < 3x + 36
Now, let's isolate x:
4x - 3x < 36
x < 36
Therefore, the smaller number 'x' is less than 36.
To find the larger number, we can substitute the value of x into equation 1:
y = x + 18
y = 36 + 18
y = 54
Therefore, the smaller number is less than 36, and the larger number is 54.