An algebra problem by Vishnu Kadiri

Algebra Level 2

There are two numbers whose sum is 9 times their difference. And the difference of their squares is 81. Find the greater number.


The answer is 15.

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1 solution

Noel Lo
Jul 12, 2015

Let the two numbers be x x and y y .

x + y = 9 ( x y ) x+y = 9(x-y)

x 2 y 2 = 81 x^2 - y^2 =81

( x + y ) ( x y ) = 81 (x+y)(x-y) = 81

9 ( x y ) ( x y ) = 81 9(x-y)(x-y) = 81

( x y ) 2 = 9 (x-y)^2 = 9

x y = 3 x-y = 3

x + y = 9 ( 3 ) = 27 x+y = 9(3) = 27

2 x = 30 2x = 30

x = 15 x = \boxed{15}

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