matj
posted by evelyn .
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.

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.