SOLUTION: Eddie, Felix and Gerald shared a stack of cards. Felix received 1/2 of the stack of cards. Gerald received 104 fewer cards than Felix. Eddie received 2/5 of what Felix and Geral

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Eddie, Felix and Gerald shared a stack of cards. Felix received 1/2 of the stack of cards. Gerald received 104 fewer cards than Felix. Eddie received 2/5 of what Felix and Geral      Log On


   

Question 1184095: Eddie, Felix and Gerald shared a stack of cards.
Felix received 1/2 of the stack of cards.
Gerald received 104 fewer cards than Felix.
Eddie received 2/5 of what Felix and Gerald received.
a) What fraction of the stack of cards was Gerald’s share?
b) How many cards did the boys have altogether?
Sos
Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of cards. Then

Felix got half of them: %281%2F2%29x
Gerald got 104 less than Felix: %281%2F2%29x-104
Eddie got 2/5 as many as Gerald and Felix together: %282%2F5%29%28x-104%29

Adding the number each got gives the total number:

%281%2F2%29x%2B%281%2F2%29x-104%2B%282%2F5%29%28x-104%29=x
x-104%2B%282%2F5%29%28x-104%29=x
%282%2F5%29%28x-104%29=104
x-104=%285%2F2%29%28104%29=260
x=260%2B104=364

Felix got (1/2)x = 182
Gerald got 104 fewer = 78
Eddie got 2/5 as many as Felix and Gerald together = (2/5)(260)=104

182+78+104=364

ANSWERS:

Gerald's share was 78 (or 78/364=3/14)
The total number was 364