Posted by evelyn on Friday, October 1, 2010 at 4:27pm.
The difference of two numbers is 12. Two fifths of the greater number is six more than onethird of the lesser number. Find both numbers.

matj  Henry, Friday, October 1, 2010 at 7:23pm
x  y = 12,
2x/5 = y/3 + 6,
Multiply both sides by 15, the common denominator:
6x = 5y + 90,
6x  5y = 90,
Multiply both sides of 1st Eq by 6 and add the 2 Eqs:
x  y = 12
6x  5y = 90
6x + 6y = 72
6x  5y = 90
y = 18,
Substitute 18 for y in the 1st Eq:
x  18 = 12,
x = 30.
Solution set: x = 30, and y = 18.
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