The organisers of an essay competition decide that a winner in thecompetition gets a prize of ` 100 and a participant who does not win getsa prize of ` 25. The total prize money distributed is ` 3,000. Find thenumber of winners, if the total number of participants is 63.
Question
The organisers of an essay competition decide that a winner in thecompetition gets a prize of 100 and a participant who does not win getsa prize of 25. The total prize money distributed is ` 3,000. Find thenumber of winners, if the total number of participants is 63.
Solution
Let's denote the number of winners as 'w' and the number of participants who did not win as 'p'.
From the problem, we know that:
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The total number of participants is 63. This can be expressed as: w + p = 63.
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The total prize money distributed is
3,000. Given that each winner gets100 and each participant who does not win gets ` 25, this can be expressed as: 100w + 25p = 3000.
We now have a system of two equations, and we can solve it step by step.
Step 1: Multiply the first equation by 25 to make the coefficients of 'p' the same in both equations. This gives us: 25w + 25p = 1575.
Step 2: Subtract the new equation from the second equation: 100w + 25p - (25w + 25p) = 3000 - 1575. This simplifies to 75w = 1425.
Step 3: Solve for 'w' by dividing both sides of the equation by 75: w = 1425 / 75 = 19.
Step 4: Substitute 'w' = 19 into the first equation: 19 + p = 63. Solving for 'p' gives: p = 63 - 19 = 44.
So, there are 19 winners and 44 participants who did not win.
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