Benediktov Problem: Solve the Daughters' Egg Selling Challenge

[vikasj007]

Hey, I once read this problem, but still can't find the solution to it.
It goes like this,

One women made a living by selling eggs, had 90 eggs which she wanted her three daughters to sell. So she gave her eldest daughter 10 eggs, 30 to her second daughter and 50 to the youngest.

'You better agree among yourselves', she told them, ' about the price you're going to ask fo you eggs, and stick to it. But I hope that the eldest will receive as much for her 10 eggs as the second will for her 30 eggs and the third for her 50 eggs. In other words each of you should bring back the same amount of money and keep in mind, the total for 90 eggs should not be less than 90 bucks.'

Although Benediktov says that the daughters were smart enough to find a way out, but I guess I am not that smart.

so kindly help me in getting a solution for this.

 

[HallsofIvy]

I'm not sure how one should interpret this! (For one thing there was no problem stated. You say "the daughters were smart enough to find a way out" but out of what? What are we to do? I assume we are to determine how much each daughter was to charge for eggs but that was not stated.

From "'You better agree among yourselves', she told them, ' about the price you're going to ask fo you eggs, and stick to it.'" I would have thought they were all to sell for the same price (per egg) but then "But I hope that the eldest will receive as much for her 10 eggs as the second will for her 30 eggs and the third for her 50 eggs." seems to contradict that- unless this is "as much per egg" which doesn't seem likely- in that case, there is no reason for that second sentence.

Anyway, if we assume that "as much for here 10 eggs",etc. means total eggs, then she is saying that she hopes each will make the same amount in total. Since she expects " the total for 90 eggs should not be less than 90 bucks.", we want the total to be at least $90. Okay, 1/3 of that is $30 so the first daughter must charge $3 for each of her 10 eggs, the second $1 for each of her 30 eggs and the third daughter $0.60 for each of her 50 eggs. Doesn't sound very likely to me.

If the interpretation "the daughters sell their eggs for the same price per egg" is correct, then obviously each should sell her eggs for at least $1 per egg- which is much too easy and also doesn't make much sense.

Could you please give us the problem exactly the way it is given in the book?

 

[M98Ranger]

Sure, I can help you solve the Daughters' Egg Selling Challenge. The key to solving this problem is to understand that the total amount of money earned from selling the eggs must be equal to or greater than 90 dollars. Additionally, each daughter must receive the same amount of money for their respective number of eggs.

To start, let's assign a hypothetical price for the eggs, say $1 per egg. This means that the eldest daughter would earn $10 for her 10 eggs, the second daughter would earn $30 for her 30 eggs, and the youngest daughter would earn $50 for her 50 eggs. In total, they would earn $90, which meets the minimum requirement.

However, this solution does not meet the second requirement of each daughter receiving the same amount of money. To adjust for this, we can increase the price of the eggs for the eldest daughter and decrease it for the youngest daughter. For example, if we increase the price to $2 for the eldest daughter's eggs and decrease it to $0.50 for the youngest daughter's eggs, they would each earn $20 for their respective number of eggs, while the second daughter would still earn $30 for her 30 eggs. This would result in a total of $70, which is less than the minimum requirement of $90.

To make up for this difference, we can add an extra $20 to the total by increasing the price for the eldest daughter's eggs to $2.50, keeping the price for the second daughter's eggs at $1, and decreasing the price for the youngest daughter's eggs to $0.50. This would result in each daughter earning $25 for their respective number of eggs, and the total would be $90, meeting the minimum requirement.

Therefore, the solution to the Daughters' Egg Selling Challenge is as follows: the eldest daughter sells her eggs for $2.50 each, the second daughter sells her eggs for $1 each, and the youngest daughter sells her eggs for $0.50 each. This way, each daughter earns $25, and the total earned from selling 90 eggs is $90, as required. I hope this helps you understand the solution and you can now solve the problem on your own.