# Thread: Easy (although hard for me) math problem

1. ## 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.

2. Hello, DiscreteW!

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

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?

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

Not sure what this says or what to do now.
Note that 29, 593, and 599 are primes.

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

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

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

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

Since the price was the same on both days,

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