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 amount of his paychecks for the year?
A) $752
B) $755
C)$765
D) $773
E) $775
The answer explanation only shows how you could solve this by calculating it out in full... i.e. working out (6(750)+20(780))/26. I can ballpark it down to 2 answers right off the bat, noticing that the average is weighted on the 780 paycheck side, but that is as far as I can go w/o calculation. Is there a better way, not involving time consuming calculation, to find the answer here?
Can you do this problem w/o any calculation?
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I guess we can do this w/o calculation.
if each month he had received 750, hen the average wud be 750. He received 30*20 =600 hundred dollars extra.
this 600 dollars must be divided into 26 parts to egt the average.600/26= 23.something
answer is 750+23=773
if each month he had received 750, hen the average wud be 750. He received 30*20 =600 hundred dollars extra.
this 600 dollars must be divided into 26 parts to egt the average.600/26= 23.something
answer is 750+23=773
The powers of two are bloody impolite!!
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Let's start with rapid elimination:phaedrus82 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 amount of his paychecks for the year?
A) $752
B) $755
C)$765
D) $773
E) $775
The answer explanation only shows how you could solve this by calculating it out in full... i.e. working out (6(750)+20(780))/26. I can ballpark it down to 2 answers right off the bat, noticing that the average is weighted on the 780 paycheck side, but that is as far as I can go w/o calculation. Is there a better way, not involving time consuming calculation, to find the answer here?
765 is the midpoint between 750 and 780. 780 "weighs more" in the average, so the answer MUST be more than 765... eliminate A, B and C.
Now let's think about D and E. 775 (the easier number) is 5/6 of the way from 750 to 780. 775 would only be the right answer if 5/6ths of the paychecks were for 780. Does 20/26=5/6? No! Therefore, 775 cannot be the right answer... eliminate E.
Only one choice left - choose D!
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