Luke developed a game for phones that he sold for $5. After the first week he discovered he had 1,916 downloads from girls and 6 times as many boys download the game. Of the boys who downloaded it he only had 1/2 who bought the full game. How many boys bought the full game?
We know the number of boys who downloaded the game is\(1,916 \times 6 = 11,496\).
But, only half of these bought the full game, so only \(11496 \div 2 = \color{brown}\boxed{5,748}\) boys downloaded the game.