There are two numbers whose sum is 9 times their difference. And the difference of their squares is 81. Find the greater number.
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Let the two numbers be x and y .
x + y = 9 ( x − y )
x 2 − y 2 = 8 1
( x + y ) ( x − y ) = 8 1
9 ( x − y ) ( x − y ) = 8 1
( x − y ) 2 = 9
x − y = 3
x + y = 9 ( 3 ) = 2 7
2 x = 3 0
x = 1 5