Topic: Hello from Diophantine
 Message: Posted by: Nir Dahan (Aug 22, 2007 02:50PM)
Mr D. had a clothing store.

previously the shirts were \$2.00 each.
D. decided to discount the shirts and after that move sold the entire lot.
The gross from the entire sale was \$603.77
how many shirts were sold?
 Message: Posted by: Roland78 (Aug 22, 2007 06:06PM)

D.
 Message: Posted by: Psy-Kosh (Aug 22, 2007 06:55PM)
60377/x = y, x and y positive integers, x < 200

60377 = 173 * 349

349 were sold at a cost of \$1.73 each
 Message: Posted by: magicgeorge (Aug 22, 2007 08:59PM)
Hi Psy,
How did you get from the first line to the second?
Are they the only two multiples of 60377 (with one less than 200(don't think that makes a difference though))?

george
 Message: Posted by: Psy-Kosh (Aug 22, 2007 10:40PM)
173 and 349 are both prime, so 173*349 is the prime factorization of 60377, and the only divisors other than the number itself and 1.

So since only one of those numbers is less than 200, and since we know the price has to be less than 200 cents, well, there we go.

That make sense?
 Message: Posted by: magicgeorge (Aug 23, 2007 04:25AM)
Yup. Cheers.