Solution to the Problem: No. $700 will not be enough for the retailer to purchase 11 copies of the International Affairs book and 5 copies of the Crime Fiction novel.
Explanation:
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Let the respective cost of one copy of the International Affairs book and one copy of the Crime Fiction novel be n dollars and c dollars.
Then by the given conditions we must have:
340n < 620c < 341n ............(i)
Now, from (i), we have:
17n < 31c, and 20c < 11n
Therefore, we must have :
17n+1 ≤ 31c .............(ii)
20c ≤ 11n -1 .............(iii)
Multiplying (ii) by 20 and (iii) by 31, we have:
340n+20 ≤ 620c ≤ 341n - 31
or, n≥ 51
Then, in terms of (ii), we must have:
31c ≥ 17n+1 ≥ 17*51 +1 = 868
or, c ≥ 28
Therefore, we have:
11n+5c ≥ 11*51 + 5*28 = 701
Accordingly, the retailer would require at least $701 to buy the requisite number of copies of the two items.
Consequently, $700 will not be enough for the wholesaler to purchase 11 copies of the International Affairs book and 5 copies of the Crime Fiction novel.
Here is Ritwik Chaudhuri's solution:
