Carcass wrote:
Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?
(A) $752
(B) $755
(C) $765
(D) $773
(E) $775
\(\frac{{750 + \cdots + 750 + 780 + \cdots + 780}}{26}\)
\(=\frac{{750 \cdot 6 + 780 \cdot 20}}{26}\)
\(=\frac{{4500 + 15600}}{26}\)
\(=\frac{20100}{26}\)
\(=773.0769\)
Therefore, D is the right answer.