a student playing a computer chess game gets 5 points every time he wins a round.the computer gets 3 points every time it wins a round.they play 64 rounds and end with a tied score.how many rounds did the computer win.
please help me ..
i think the answer is 8 because...
5+3=8
64/8=8
3*8=24
5*8=40
40+24=64
i don't know if that's the answer
let the number of your wins be x
then the number of computer wins is 64-x
5x = 3(64-x)
5x = 192 - 3x
8x = 192
x = 24
students wins 24 games, computer wins 40 games
test:
5x24 = 120
3x40 = 120
To solve this problem, we need to consider that the student gets 5 points for every win, and the computer gets 3 points for every win. Let's break it down step by step.
1. Let's assume the computer won x number of rounds. So, the student won 64 - x rounds since they tied in the end.
2. The total points earned by the student would be 5 times the number of wins: 5 * (64 - x).
3. The total points earned by the computer would be 3 times the number of wins: 3 * x.
4. Since the total points are equal because it's a tie, we can set up an equation:
5 * (64 - x) = 3 * x
5. Let's solve for x:
320 - 5x = 3x
320 = 8x
x = 320 / 8
x = 40
So, the computer won 40 rounds, which means the student won 64 - 40 = 24 rounds.
Therefore, the computer won 40 rounds.