The given solution is indeed faster, direct and less error prone.
Bunuel
Official Solution:A music store has 90 different CDs. If the average (arithmetic mean) price of a CD is $12, and 20 of the most expensive CDs cost $20 each, what is the average (arithmetic mean) price of the remaining CDs?A. 8.33
B. 8.75
C. 9.23
D. 9.71
E. 10.07
The total cost of all CDs is \(90*$12 = $1,080\).
The total cost of the 20 most expensive CDs is $400. Subtracting this from the total, we have \($1,080 - $400 = $680\) allocated for the remaining 70 CDs. Hence, the average price of these CDs is \(\frac{$680}{70} = $9.71\).
Answer: D
I was trying with weighted average method:
assuming x as the average of 70 remaining,
(12-x)/(20-12) = 20/70 => (12-x)/8 = 2/7 => x = 68/7 = 9.7.