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Question Number 125915 by john_santu last updated on 15/Dec/20

Darren McFaddden of Arkansas  placed second overall in the Heisman  Trophy voting. Players are given  3 points for every first−place vote   , 2 points for every second−place vote  and 1 point for every third−place vote.  McFadden received 490 total votes  for first , second and third place   for a total 878 points . If he had  4 more than twice as many second  −place votes as third−place votes, how  many votes did he received for  each place?

$${Darren}\:{McFaddden}\:{of}\:{Arkansas} \\ $$$${placed}\:{second}\:{overall}\:{in}\:{the}\:{Heisman} \\ $$$${Trophy}\:{voting}.\:{Players}\:{are}\:{given} \\ $$$$\mathrm{3}\:{points}\:{for}\:{every}\:{first}−{place}\:{vote}\: \\ $$$$,\:\mathrm{2}\:{points}\:{for}\:{every}\:{second}−{place}\:{vote} \\ $$$${and}\:\mathrm{1}\:{point}\:{for}\:{every}\:{third}−{place}\:{vote}. \\ $$$${McFadden}\:{received}\:\mathrm{490}\:{total}\:{votes} \\ $$$${for}\:{first}\:,\:{second}\:{and}\:{third}\:{place}\: \\ $$$${for}\:{a}\:{total}\:\mathrm{878}\:{points}\:.\:{If}\:{he}\:{had} \\ $$$$\mathrm{4}\:{more}\:{than}\:{twice}\:{as}\:{many}\:{second} \\ $$$$−{place}\:{votes}\:{as}\:{third}−{place}\:{votes},\:{how} \\ $$$${many}\:{votes}\:{did}\:{he}\:{received}\:{for} \\ $$$${each}\:{place}? \\ $$$$ \\ $$

Answered by liberty last updated on 15/Dec/20

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