After playing the first 25% of his tennis matches this seasons, Colin won 20% of his matches. What percent of his remaining matches must he win to win 50% of his matches ?
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total matches ..... x
matches played so far .... x/4
matches won so far = (1/5)(x/4) = x/20
let remaining percentage he wins = y%
(y/100)(3x/4) + x/20 = x/2
divide by x
(y/100)(3/4) + 1/20 = 1/2
multiply by 400
3y + 20 = 200
3y = 180
y = 60
To find out what percent of his remaining matches Colin must win to win 50% of his matches overall, we can break it down into steps:
Step 1: Calculate the total number of matches played so far.
Since Colin has played the first 25% of his matches, we can assume that the remaining 75% of matches are yet to be played. Let's say the total number of matches in the season is 'x'. Therefore, the total number of matches played so far is 25% of 'x': 0.25x.
Step 2: Calculate the total number of matches Colin needs to win to reach 50%.
To win 50% of his matches overall, Colin needs to win half of the total matches played. Since he has already played 25% of the matches, he needs to win an additional 25% to reach 50%. So the number of matches Colin needs to win is: 25% of 'x' - 20% of 'x', which simplifies to 5% of 'x'.
Step 3: Calculate the number of remaining matches.
Since Colin has played 25% of the matches, the number of remaining matches would be the remaining 75% of 'x': 0.75x.
Step 4: Calculate the percent of remaining matches Colin needs to win to reach 50%.
To calculate the percent of remaining matches Colin needs to win, we divide the number of matches he needs to win by the number of remaining matches, and then multiply the result by 100 to convert it to a percentage. So the calculation is: (5% of 'x') / (0.75x) * 100.
Simplifying this expression gives: (5/0.75) * 100 = 6.67 * 100 = 666.67%.
Therefore, Colin must win approximately 66.67% of his remaining matches to win 50% of his matches overall.