# Easy (although hard for me) math problem

• Nov 10th 2008, 06:49 AM
DiscreteW
Easy (although hard for me) math problem
I have no idea how to do this...

Suppose that on Wednesday a ipod company earns $17197 from selling ipods @ an even dollar price which is greater than$1 and on Thursday the ipod store earns $17371 from selling ipods @ that same even dollar price as on Wednesday. Determine the number of ipods the company sold each day and @ what even dollar price (greater than$1)?

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So I'm confused by this "even dollar" thing.

I thought of just finding the GCD(17197, 17371) which is 29, then dividing each of those numbers by it...

So 17197/29 = 593 and 17371/29 = 599

Not sure what this says or what to do now. Thanks for the help.
• Nov 10th 2008, 07:58 AM
Soroban
Hello, DiscreteW!

You found the answers . . . you just didn't recognize them.

Quote:

On Wednesday a company earned $17197 from selling ipods at an even dollar price and on Thursday the company earned$17371 from selling ipods at that same price.
Determine the number of ipods the company sold each day and at what price?

- - - - - - - -

So I'm confused by this "even dollar" thing.
. .
I'm sure it means "whole dollar" price.

I thought of just finding the GCD(17197, 17371) which is 29,
then dividing each of those numbers by it. . . . . Good!

So: . $17197 \div 29 \:= \:593\:\text{ and }\;17371 \div 29 \:=\: 599$ . . . . Yes!

Not sure what this says or what to do now.

Note that 29, 593, and 599 are primes.

Since $17197 \:=\:29\cdot593$, then on Wednesday,

. . the store sold: . $\begin{Bmatrix} 29\text{ ipods at }\593\text{ each} \\ \text{or} \\ 593\text{ ipods at }\29\text{ each} \\ \end{Bmatrix}$

Since $17371 \:=\:29\cdot599$, then on Thursday,

. . the store sold: . $\begin{Bmatrix}29\text{ ipods at }\599\text{ each} \\ \text{or} \\ 599\text{ ipods at }\29\text{ each} \end{Bmatrix}$

Since the price was the same on both days,

. . $\begin{array}{ccc}\text{Wedmesday} & 593\text{ ipods at }\29\text{ each} \\ \text{Thursday} & 599\text{ ipods at }\29\text{ each} \end{array}$