MHB Solve Mr. Denis & Joppy's Goats Weight Difference Problem

[Monoxdifly]

Mr. Denis has 5 goats with the average weight 36 kg while Mr. Joppy has 5 goats with the average weight 34 kg. If they exchange one of their goats so that their overall average weight is equal, what is the weight difference of their switched goats? I only know that Mr. Denis' goats' total weight is 180 kg and Mr. Joppy's is 170 kg. How to do it from there?

 

[MarkFL]

What is the combined weight of all 10 goats? How much should each man have then if both are to have the same weight?

 

[Monoxdifly]

The combined weight of 10 goats is 350 kg and each man should have 35 kg per goat.

 

[MarkFL]

Yes, so each man should have a combined weight of (350/2) kg = 175 kg in goat weight. How much does each man need to gain/lose...that is, what should the difference in the weights of the two traded goats be?

 

[Monoxdifly]

1 kg?

 

[MarkFL]

1 kg?

How did you arrive at that?

 

[Monoxdifly]

How did you arrive at that?

Sorry, I mean 1 kg per person. So, the difference must be 2 kg.

 

[MarkFL]

If Mr. D has 180 kg and Mr. J has 170 kg, then for them to both have the same weight, Mr. D needs to lose 5 kg while Mr. J needs to gain 5 kg. This way they will both have 175 kg.

 

[Monoxdifly]

So, the answer is 10 kg?

 

[MarkFL]

So, the answer is 10 kg?

No, they need to exchange two goats whose difference in mass is 5 kg.

 

[Monoxdifly]

Oops, sorry. Thanks for the answer.
Geez,what happened to my brain?