Final answer:
To find out what percent of his remaining matches Colin must win to have won 50% of his matches, we set up an equation and solve for the percentage. The answer is 60%.
Step-by-step explanation:
To solve this problem, we need to first determine how many matches Colin has played and how many matches he has won. If he has played 25% of his matches for the year, it means he has played 0.25x matches, where x is the total number of matches.
Next, we need to find out how many matches he has won. If he has won 20% of the matches he played, it means he has won 0.2 * 0.25x = 0.05x matches.
To calculate the remaining matches, we subtract the matches Colin has played from the total matches for the year: Remaining matches = x - 0.25x = 0.75x.
To find out what percent of his remaining matches Colin must win to have won 50% of his matches, we set up the following equation:
0.05x + (Percent of remaining matches won) * 0.75x = 0.5x
Simplifying the equation, we have:
0.05x + (Percent of remaining matches won) * 0.75x = 0.5x
0.05 + 0.75(Percent of remaining matches won) = 0.5
0.75(Percent of remaining matches won) = 0.5 - 0.05
0.75(Percent of remaining matches won) = 0.45
(Percent of remaining matches won) = 0.45 / 0.75
(Percent of remaining matches won) = 0.6
To express this as a percentage, we multiply by 100:
(Percent of remaining matches won) = 0.6 * 100
(Percent of remaining matches won) = 60%