Billy was playing a trivia game. According to the rules, Billy would receive 25 points for each question he answered correctly but would lose 50 points for each question he answered incorrectly. At the end of the game, Billy had a total of 450 points. He had 5 times as many questions correct as incorrect. If Billy answered every question, how many questions were asked in the game?

Question

Billy was playing a trivia game. According to the rules, Billy would receive 25 points for each question he answered correctly but would lose 50 points for each question he answered incorrectly. At the end of the game, Billy had a total of 450 points. He had 5 times as many questions correct as incorrect. If Billy answered every question, how many questions were asked in the game?

Answer 1

number of wrong --- x

number of rights ---- 5x

25(5x) - 50x = 450

solve for x

Answer 2

To solve this problem, let's break it down into steps:

1. Let's assume the number of questions Billy answered correctly is x.
2. According to the information given, Billy receives 25 points for each question he answers correctly. Therefore, the total points earned from answering correctly is 25x.
3. Billy also loses 50 points for each question he answers incorrectly. So, the total points deducted for answering incorrectly is 50 * (5x/5) = 50x.
Since Billy had a total of 450 points, we can now write the equation:
25x - 50x = 450.
4. Simplifying the equation, we have -25x = 450.
5. Dividing both sides of the equation by -25, we get x = -18.
Since the number of questions answered correctly cannot be negative, we can conclude that we made an error in our assumption.
6. Let's correct our assumption: Billy answered 5 times as many questions correctly as incorrectly. Therefore, the number of questions Billy answered incorrectly is x/5.
7. As per the information given, the total points earned from answering correctly is 25x, and the total points deducted for answering incorrectly is 50 * (x/5) = 10x.
We can now write the equation: 25x - 10x = 450.
8. Simplifying the equation, we have 15x = 450.
9. Dividing both sides of the equation by 15, we get x = 30.
Therefore, Billy answered 30 questions correctly.
10. The number of questions answered incorrectly is x/5 = 30/5 = 6.
11. To find the total number of questions asked in the game, we need to add the number of questions Billy answered correctly (30) and incorrectly (6).
Therefore, the total number of questions asked in the game is 30 + 6 = 36.

So, there were 36 questions asked in the game.