SOLUTION: The difference of the numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find the numbers.

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Question 104442: The difference of the numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find the numbers.
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
In this problem, we are finding two unknowns. So we shall
Let x=the greater number
y=the smaller number
The difference of the numbers is 12.
So, x-y=12
From which, x=y+12
Two fifths of the greater number is six more than one third of the lesser number
So, %282%2F5%29%2Ax=%281%2F3%29%2Ay%2B6
To eliminate the fractions, let us multiply both sides by 15.
15%2A%28%282%2F5%29%2Ax%29=15%2A%28%281%2F3%29%2Ay%2B6%29
~~~~~~6x=5y%2B30

But, x=y+12, so,
6%2A%28y%2B12%29=5y%2B30
~~~6y%2B72=5y%2B30
Subtracting 30 both sides,
6y%2B42=5y
~y%2B42=0
~~~~y=-42
Again, x=y+12, so,
x=y+12
x=-42+12
x=-30

Therefore, the two numbers are -30 and -42!