Given that a and b are positive integers and that a + b = 24 , what is the value of ab if 2ab + 10a = 3b + 257 ?
+40 a + b = 24 so b = 24 - a
Sub this into the other equation
2a (24 - a) + 10a = 3(24 - a) + 257
48a - 2a^2 + 10a = 72 - 3a + 257
-2a^2 + 58a = 329 - 3a
2a^2 - 61a + 329 = 0
(2a - 47)(a - 7) = 0
only one of the solutions for a is an integer and it is 7
7 + b = 24
b = 17
(7)(17)=119
