In a contest the prizes were to be $100 for the first place, $50 for second and $20 for the third. Instead, there was 2-way tie for the first place and one third place. If each first prize is twice the value of the third place award, how much did each first place prize winner ...
math problem...
- Thread starter ladoo
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- Apr 12, 2005
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One answer might be $60, but then we ahve not given away all the prize money. These MIGHT be the contest rules. One woul dhave to read VERY CAREFLLY to know the specific rules.
Let's assume the rule is to distribute ALL the funds - the total prize will remain unchanged.
Let's define:
T = Third Place Prize
F = First Place Price
We know that F = 3T
We know that T + 2F = 100 + 50 + 20 = 170 = T + 2(3T) = 7T
This gives T = 170/7 = 24.28 <== Truncating, rather than rounding, because most of the contestants don't understand why the 3rd place guy gets more money.
Finally, F = 3T = 3(24.28) = 72.84
Of course, 24.28 + 72.84 + 72.84 = 169.96, so we are still 4¢ short.
Perhaps: 23.28, 72.85, and 72.85 will do it.
Can you see another solution or have we arrived at a unique conclusion? If it is unique, it is because we added the assumption about the total prize money. That was NOT in the original problem statment, so we will need to leave some room for other assumptions and solutions.
Let's assume the rule is to distribute ALL the funds - the total prize will remain unchanged.
Let's define:
T = Third Place Prize
F = First Place Price
We know that F = 3T
We know that T + 2F = 100 + 50 + 20 = 170 = T + 2(3T) = 7T
This gives T = 170/7 = 24.28 <== Truncating, rather than rounding, because most of the contestants don't understand why the 3rd place guy gets more money.
Finally, F = 3T = 3(24.28) = 72.84
Of course, 24.28 + 72.84 + 72.84 = 169.96, so we are still 4¢ short.
Perhaps: 23.28, 72.85, and 72.85 will do it.
Can you see another solution or have we arrived at a unique conclusion? If it is unique, it is because we added the assumption about the total prize money. That was NOT in the original problem statment, so we will need to leave some room for other assumptions and solutions.