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

Question 306622: The difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find both numbers.
Answer by sejackson91(8) (Show Source): You can put this solution on YOUR website!
first write out the words they give you as equations
the difference of two numbers is 12 means that
A - B = 12 if A and B are our two numbers
then two fifths of the greater number is six more than one third of the lesser number
the second part can be broken up to make it easier to understand
say that A is the greater number
two fifths is 2/5
so two fifths of the greater number is (2/5)A remember that in these word problems of means you need to multiply
next this (2/5)A is 6 more than something so say that (2/5)A - 6 = this something
the something is one third of the lesser number so it is (1/3)B
finally:
(2/5)A - 6 = (1/3)B
now we need to find the two numbers using the two equations we wrote:
A - B = 12
(2/5)A - 6 = (1/3)B
looking at the first equation we see that A = 12+B
we can substitute that into the second equation
(2/5)(12+B) - 6 = (1/3)B
(24/5) + (2/5)B - (30/5) = (1/3)B

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