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?
just add/subtract the points! If he had x incorrect, then he had 5x correct, so
5x*25 - 50x = 450
total questions: x+5x=6x
To solve this problem, we need to set up some equations and solve for the number of questions asked in the game.
Let's define the following variables:
C = number of questions Billy answered correctly
I = number of questions Billy answered incorrectly
According to the problem statement, Billy received 25 points for each question he answered correctly, so the number of points he received from correct answers is 25C.
Similarly, Billy lost 50 points for each question he answered incorrectly, so the number of points he lost from incorrect answers is 50I.
Based on this information, we can set up the following equation for the total number of points Billy had at the end of the game:
25C - 50I = 450 (equation 1)
The problem also states that Billy had 5 times as many questions correct as incorrect, so we can write another equation: C = 5I (equation 2)
Now we can solve this system of equations to find the values of C and I.