# matj

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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.

• matj -

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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