I can't work out the why to this problem

[StaRz]

I can't work out the "why" to this problem

Hi, I have (and most of you guys probably have) this problem my math teacher gave me and it is :

One man sells neckties at the price of two for $10, another sells three for $10. They decide to go into business together, and each contributes 30 ties. This gives them an inventory of 60 ties, Which they will sell at the price of five for $20- because that's the same as two ties for $10 and three ties for $10. After all 60 ties are sold, the men find that they've earend a total of $240, or the price of five ties for $20 sold to 12 customers

That evening, they go home to their wives, who proceed to tell them how dumb they were. If the first man had sold his 20 ties separately (at two for $10), he would have earened $150, and if the second man had done the same (at three for $10) he would have earened $100 - a combined total of $250, instead of $240.

Where did the $10 go?



I found out that 30 * (5 + 3.33) gives u more than 60 * 4 so they are basically losing 60 cents per tie if they sell them combined. But I don't know WHY.

Help please

 

[BobG]

Because they used the average of the two average prices instead of a true average when they came up with their plan.

One person averaged 3.33 per tie. The other averaged 5.00 per tie. The average of the two averages was 4.16 per tie. That would have worked okay if each price factored equally in the sale. The 3.33 price was factored in 3 times per sale, while the 5.00 price was only factored in twice, lowering the true average to 4.00 per tie.

In other words, to have 3:2 ration, the salesman who normally sold his ties at 5.00 a piece lowered the price on ten of his ties to match the 3.33 per tie salesman.

 

[wais]

Hi there,

It seems like you have already done some calculations to figure out where the $10 went. That's great! The reason why the $10 is "lost" is because when the men sell their ties at the price of five for $20, they are essentially selling them at a discounted rate compared to if they had sold them separately. In other words, they are selling more ties for less money. This results in a lower total profit for them.

To understand this better, let's break it down. If the first man sells his 20 ties separately at two for $10, he would make $100. But when he combines his ties with the second man's and sells them at five for $20, he is getting less money per tie - $4 instead of $5. This means that for every 5 ties they sell, they are losing $1 ($5 - $4). And since they are selling a total of 60 ties, they are losing $12 ($1 x 12) in total. This is where the $10 is going.

I hope this helps clarify things for you. Keep up the good work with your math problems!