Challenging Logic Question!

How best can I approach this logic question?

Six pairs of shoes cost as much as 1 coat, 2 pairs of jeans cost as much as 3 pairs of shoes, and 4 pairs of socks cost as much as one pair of jeans. How many coats could I exchange for 64 pairs of socks?

Re: Challenging Logic Question!

Let $\displaystyle x$=the cost of one pair of shoes

$\displaystyle y$=the cost of 1 coat

$\displaystyle z$=the cost of 1 pair of jeans

$\displaystyle t$=the cost of 1 pair of socks.

We have:

$\displaystyle 6x=y$

$\displaystyle 2z=3x$

$\displaystyle 4t=z$

Then

$\displaystyle y=6x=4z=16t\Rightarrow 4y=64t$

So we have to exchange 4 pairs of coats for 64 pairs of socks.

Re: Challenging Logic Question!

Hello, KayPee!

I avoided varaiables ... too confusing.

(I would have used initials, but we have Shoes and Socks.)

Quote:

Six pairs of shoes cost as much as 1 coat.

2 pairs of jeans cost as much as 3 pairs of shoes.

4 pairs of socks cost as much as one pair of jeans.

How many coats could I exchange for 64 pairs of socks?

We are told: .$\displaystyle \begin{Bmatrix}6\text{ shoes} &=& 1\text{ coat} & [1] \\ 2\text{ jeans} &=& 3\text{ shoes} & [2] \\ 4\text{ socks} &=& 1\text{ jean} & [3] \end{Bmatrix}$

$\displaystyle \begin{array}{cccccccc}\text{Multiply [3] by 4:} & 16\text{ socks} &=& 4\text{ jeans} & [4] \\ \text{Multiply [2] by 2:} & 4\text{ jeans} &=& 6\text{ shoes} & [5] \\ \text{And we have [1]:} & 6\text{ shoes} &=& 1\text{ coat} & [6] \end{array}$

Equate [4], [5] and [6]: .$\displaystyle 16\text{ socks} \:=\:1\text{ coat}$

. . . . . . . . . .Multiply 4: .$\displaystyle 64\text{ socks} \:=\:4\text{ coats}$

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An unfortunate choice of items of clothing.

Someone may feel obligated to mention the *two* shoes

. . and the *two* socks in each pair.

Yet "a pair of jeans" involves only *one* item of clothing.

(They are singular at the top, plural at the bottom.)

Our language has many pseudo-pairs: a pair of pants,

. . a pair of slacks, a pair of scissors, a pair of pliers.

One would think that *brassiere* would be referred to in pairs;

. . the concept of *two* is so strongly suggested.

(Okay, maybe it's because I'm a guy . . .)