+612 Given that $a$ and $b$ are positive integers and that $a+b=24$, what is the value of $ab$ if $2ab + 10a = 3b + 222$?
+129852 Given that $a$ and $b$ are positive integers and that $a+b=24$, what is the value of $ab$ if $2ab + 10a = 3b + 222$?
a + b = 24 so b = 24 - a
Sub this into the other equation
2a (24 - a) + 10a = 3(24 - a) + 222 simpllify
48a - 2a^2 + 10a = 72 - 3a + 222
-2a^2 + 58a = 294 - 3a rearrange as
2a^2 - 61a + 294 = 0 factor this as
(2a - 49)(a - 6) = 0
Only the second factor will produce an integer if set to 0 ...so a - 6 = 0 ⇒ a = 6
And b = 24 - 6 = 18
So ab = 6*18 = 108
