To win a brand new Bible at Tom Sawyer's Sunday school, a pupil has to win 10 yellow tickets; each yellow ticket is obtained by trading in 10 red tickets; each red ticket is obtained by trading in 10 blue tickets; and blue tickets are earned by memorizing two Bible verses. But rather than go to all that trouble, Tom Sawyer has traded various toys and treasures of his with his friends until he has gathered 8 yellow, 3 red, and 7 blue tickets. How many more blue tickets would he need to earn to win a new Bible? Give me reasons, before answering the question
A red ticket is equal to 10 blue tickets, and a yellow is equal to ten red tickets, so a yellow ticket is also equal to 10 * 10 = 100 blue tickets. It takes 10 yellow tickets to win a Bible, or 10 * 100 = 1000 blue tickets. Tom has 8 yellow tickets, which are worth 8 * 100 = 800 blue tickets. He also has 3 red tickets, which are worth 3 * 10 = 30 blue tickets. Added with his 7 blue tickets, he has 800 + 30 + 7 = 837 blue tickets' worth of tickets. So he still needs to earn 1000 - 837 = 163 blue tickets. So the final answer is 163.