The 15 homes in a new development are each to be sold for

Fastest way to do the calculation is as shown below:
Avg = 200
so lets find the deviation from avg for each sale.

i.e for 4 homes its was -30, 5 homes it was 0 and let x be deviation for rest of the 6 homes.

setup a equation: -30*4 + 5*0 + x*6 = 0 <== (basically 0*15) find x = 20 so the homes should be sold for 220,000 of avg to converge to 200,000.

Answer: D

For the sake of calculation, remove the 3 extra zero's from the question as well as answer

\(Answer = \frac{200*15 - 170*4 - 200*5}{6} = \frac{3000 - 1680}{6} = 500 - 280 = 220\)

Answer = D = 220000

The total selling price of the 4 homes is 4 x 170,000 = $680,000, and the total selling price of the 5 homes is 200,000 x 5 = $1,000,000. Thus, the total selling price of these 9 homes is $1,680,000.

The total selling of the all 15 homes is 15 x 200,000 = $3,000,000.

Thus, the total selling price of the remaining 6 homes is 3,000,000 - 1,680,000 = $1,320,000, resulting in a price of 1,320,000/6 = $220,000 per home.

Answer: D

This is a fairly simple question on Weighted Averages. The fact that the 15 homes have been divided into three groups, each having a different pricing, is a clear give away that the Arithmetic Mean in this case will be the Weighted Average.

There are three different groups given in this question with different averages and weights. In such a situation, the weighted average can be calculated as,

A = \(\frac{A1 * N1 + A2 * N2 + A3 * N3}{N1 + N2 + N3}\), where A1, A2 and A3 represent the respective averages of the 3 groups and N1, N2 and N3 their weights.

The Arithmetic Mean for the 15 houses is given as $200,000 per home. This means that the total price of all the 15 homes is $3000,000.

Note: For easy calculation, it’s advisable to omit the 3 zeroes at the end of all prices mentioned. You can append the 3 zeroes to the final answer.

4 of the homes were sold for $170 each, so the total selling price of these homes = $680.

5 of the homes were sold for $200 each, so the total selling price of these homes = $1000.

The remaining 6 homes need to give us a total of (3000 – 1680) = $1320. Therefore, the average selling price per home for these homes = \(\frac{1320}{6}\) = 220 or in other words, $220,000.

The correct answer option is D.

Hope that helps!

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