SOLUTION: The difference between two numbers is 18. 5 times the larger number is 2 times the smaller number. Find the two numbers.

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Question 131374: The difference between two numbers is 18. 5 times the larger number is 2 times the smaller number. Find the two numbers.
Answer by TakeATuition.com(57) (Show Source):
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SOLUTION -
Let the larger number be x
and smaller number be y
therefore according to the first condition that is,"the difference between two numbers is 18" we have

x - y = 18
x = 18 + y .............. (i)
now according to the second condition we have five times the greater is equal to 2 times the smaller, we have
5x = 2y
5x = 2y
substituting the value of x from equation (i)we have
5(18 + y) = 2y
90 + 5y = 2y
5y - 2y = -90
3y = - 90
y = -90/3
y = - 30
now substituting the value of y in equation (i) we have
x = 18 + (-30)
x = 18 - 30
x = -12

therefore
larger number is x = -12
and smaller number is y = -30