U.S. and European Sock Sizes

Date: 03/23/2002 at 12:46:01
From: nomi
Subject: Word Problem

The table below relates U.S. sock sizes to European sock sizes. Which 
expression could be used to convert European size to U.S. size?

U.S       9.5   10   10.5   11   11.5   12

European   39   40    41    42    43    44

A) u = e - 20
B) u = 0.5 e - 20
C) u = 0.5 e - 10
D) u = 2e + 20

Date: 03/23/2002 at 23:32:58
From: Doctor Twe
Subject: Re: Word Problem

Hi Nomi - thanks for writing to Dr. Math.

When given multiple choices, one way to find the right choice(s) is to 
test each answer to see if it is correct. We can test choice (A) by 
plugging in the known values and seeing whether or not the equation is 
true, like this:

       u = e - 20

     9.5 = 39 - 20

     9.5 = 19

This is clearly a false statement, so we know that A can't be the 
correct answer. (Note that even if equation (A) were true for the 
first pair of numbers, we would have to test several to make sure it 
held for _all_ the numbers.) Can you test the others and find out 
which is the correct one?

We can also find the formula ourselves by looking for patterns in the 
table. notice that the U.S. shoe sizes go up by 0.5 each time the 
European sizes go up by 1, so we can say that 'a change of 0.5 u = a 
change of 1 e', or in other words, each 1 change in e changes the u 
value by 0.5. So we can write:

     u = 0.5 e + x

Notice that we use the coefficient 0.5, not 2, because changing e by 
some value changes u by half that amount. For example, if we increase 
the value by 2 (say from 40 to 42), we only change the value of u by 1 
(from 10 to 11).

Now we must figure out what the value of x is. We can do that by 
"plugging in" a pair of numbers that we know are equal from the chart, 
and solving for x. Can you do that part? Plug that x into the formula 
above, and you have your answer!

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/