+816 For (x,y), positive integers, let \(10xy+14x+15y=166\) . Find \(x+y\).
+128448 10xy + 14x + 15y = 166
Note that ( 2x + 3) ( 5y + 7) =
10xy + 15y + 14x + 21 = 166 + 21 factor the left side
(2x + 3) ( 5y + 7) = 187
Note that 187 factors as 11 * 17
So....we can let x = 4 and y = 2 and we get
(2*4 + 3) (5*2 + 7) =
(11) (17) = 187
So
10 (4 * 2) + 14(4) + 15(2) =
80 + 56 + 30 =
80 + 86 =
166
And x + y = 4 + 2 = 6
