A Science book and a Fiction novel are available from a wholeseller. Each costs an integer number of dollars. The cost of 620 copies of the Fiction novel is greater than that of 340 copies of the Science book but less than that of 341 copies of that book.

Would $700 be enough for a retailer to purchase 11 copies of the Science book and 5 copies of the Fiction novel?

We first factor 620, 340, and 341:
31*20
17*20
31*11

So 17*20S<31*20F<31*11S
Or 17S<31F while 20F<11S

Question: Is 11S + 5F <= $700?

If so, then 20F +5F < $700 or F < $28

So let F=$27 and see that $540<11S meaning 49<S

but 17S<$837 or S<50. Since no integer satisfies both, $700 is insufficient.

Posted by Eric on 2006-06-20 18:04:06