I have won exactly 72% of the 2400 puzzles that I played. What is the minuimum number of puzzles I must win before I have to win 73% of the total number of puzzles played?
To find the minimum number of puzzles you must win before you have to win 73% of the total number of puzzles played, we can use a simple calculation.
Let's assume the number of puzzles you need to win is "x."
To calculate the total number of puzzles played, you can use the equation:
Total Number of Puzzles Played = 2400 + x
If you win exactly 72% of the 2400 puzzles, this means you have won (72/100) * 2400 = 1728 puzzles.
To find the percentage of the total number of puzzles you have won, you divide the number of puzzles won by the total number of puzzles played and multiply by 100:
Percentage of Puzzles Won = (1728 / (2400 + x)) * 100
According to the question, the percentage of puzzles won should be equal to or greater than 73%. So, we can set up the equation:
(1728 / (2400 + x)) * 100 >= 73
To solve for x, we can follow these steps:
1. Divide both sides of the equation by 100:
(1728 / (2400 + x)) >= 0.73
2. Multiply both sides of the equation by (2400 + x):
1728 >= 0.73 * (2400 + x)
3. Distribute the right side of the equation:
1728 >= 1752 + 0.73x
4. Move 1752 to the left side of the equation:
1728 - 1752 >= 0.73x
5. Simplify the left side of the equation:
-24 >= 0.73x
6. Divide both sides of the equation by 0.73 (the coefficient of x):
-24 / 0.73 <= x
7. Calculate the result:
-32.87 <= x
Since the number of puzzles cannot be negative, we take the next highest integer, which is -32:
x >= -32
Therefore, the minimum number of puzzles you must win before you have to win 73% of the total number of puzzles played is 33 puzzles.