The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 8 homes? Choose the correct choice from the following
A) $200,000 B) $210,000 C) $215,000 D) $220,000 E) $230,000
IMO the answer has to be D.   5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 8 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 8x=120,000.   x=15,000.   The 8 houses are sold at $15,000 profit or at $215,000. (ANSWER $215,000)
<result>C</result>
The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 8 homes?