Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
Choose the correct choice from the following answers:
A) 191
B) 213
C) 221
D) 223
E) 226

Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 30 sell price = $ 300 + $ 30 thus , the sell price is $ 330 for each item . selling all 100 items gives the retailer . . . 100 ( $ 30 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 330 ) = $ 16.5 discount $ 313.5 = $ 300 + $ 13.5 now , the retailer makes a profit of just $ 13.5 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 13.5 ( x ) = $ 2,000 x = 2,000 / 13.5 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: D