There are two numbers whose sum is 9 times their difference. And the difference of their squares is 81. Find the greater number.
a + b = 9 (a - b)
a + b = 9a - 9b
-8a = - 10b
b = 8/10 a = 4/5 a (1)
And
a^2 - b^2 = 81 (sub in (1) for b )
a^2 - [ (4/5)a ] ^2 = 81
a^2 - (16/25)a^2 = 81
(9/25)a^2 = 81
a^2 = 81 * ( 25/9) take the positive root
a = 9 * (5 / 3 ) = 15
b = (4/5)a = 12
