student asked in Science & MathematicsMathematics · 2 months ago

# A simple solution to a percentage problem. Or is it?

A man is 6ft tall and his son is a similar solid 5ft tall; they have suits of the same style and cloth. If the weight of the man’s suit is k per cent of his weight, find the weight of the boy’s suit as a percentage of the boy’s weight. (Assume father and son have same density.) What general conclusion can be drawn about the density of cloth suitable for adults and children.

Now, solution gives 6/5 k%, which to me appears to be the ratio of the man’s height to his son’s multiplied by the original percentage of man’s weight. Although I’m sure the author is correct, this doesn’t sit well with me. It doesn’t seem to indicate anything about, for instance, the ratio of volumes of similar figures being the cube of the scale etc. If there is some short cut here that I’m missing then I’m not sure what it is. I would like to know if there is some general rule I’m missing that can derive the correct answer quickly.

As always any help to cure my inability to see the woods for the trees (I think that’s right) would be greatly appreciated.

Relevance
• fcas80
Lv 7
2 months ago

This problem is about a simple model, namely that suit weights are in proportion to body weights. This is also called direct variation.  I'm sure it is possible to create more complex models, possibly involving more complex mathematics that you haven't seen yet.  Perhaps real-world suit manufacturing indeed uses more complex models.  However, I'm assuming you are taking an algebra course that is trying to teach simple direct variation.

Do continue to think about more complex models.  But don't make your math course harder than it needs to be.  As a general rule, the law of parsimony is a  principle according to which an explanation of a thing or event is made with the fewest possible assumptions.