Fiction Novel And Science Book Problem (Posted on 2006-06-20)
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?
$ 700 would not be enough for the retailer to purchase 11 copies of the Science Book and 5 copies of the Fiction Novel from the wholeseller.
EXPLANATION:
Let the cost of one copy of the Science Book be s dollars and the cost of one copy of the Fiction Novel be n dollars.
Accordingly, 340*s < 620*n < 341*s. This in turn means that :
17s < 31n and 20n< 11s, so that:
17s + 1 <= 31n and 20n <= 11s – 1.
Multiplying the above inequalities respectively by 20 and 31, we obtain:
340s + 20 <= 620n <= 341s – 31.
This implies that 340s + 20 <= 341s – 31; so that s>=51.
Now, 17s + 1 <= 31n ;
Or, 31n>= 17s+1 >= 17*51 +1 = 868
Or, n>= 28.
Hence, 11s + 5n >= 11*51 + 5*28 = 701, which means that $ 700 would not be enough for the retailer to purchase 11 copies of the Science Book and 5 copies of the Fiction Novel from the wholeseller.
