Given that a and b are positive integers and that a + b = 24 , what is the value of ab if 2ab + 10a = 3b + 257 ?
+130081 2ab + 10a = 3b + 257
2a ( b + 5) = 3b+ 257 [ a + b = 24 ⇒ b = 24 - a ]
So
2a ( 24 -a + 5) = 3 (24 - a) + 257
2a ( 29 -a) 72 - 3a + 257
58a - 2a^2 = 329 - 3a
2a^2 - 61a + 329 = 0
(2a -47) (a - 7) = 0
Setting both factors to 0 and solving for a gives a = 47/2 (reject) or a = 7
If a = 7 then b = 17
So
ab = 7 * 17 = 119
