SOLUTION: pls help Andy, Ben and Caleb had an equal number of stamps. Andy gave 1/4 of his number of stamps to Ben before Ben gave 2/5 of his number of stamps to Caleb. Caleb then donated

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: pls help Andy, Ben and Caleb had an equal number of stamps. Andy gave 1/4 of his number of stamps to Ben before Ben gave 2/5 of his number of stamps to Caleb. Caleb then donated      Log On


   

Question 1186480: pls help
Andy, Ben and Caleb had an equal number of stamps. Andy gave 1/4 of his
number of stamps to Ben before Ben gave 2/5 of his number of stamps to
Caleb. Caleb then donated 161 stamps to charity. Caleb had 5/6 as many
stamps as Andy in the end. How many stamps did the three boys have
altogether at first?
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of stamps each boy had at the start:
Andy = x
Ben = x
Caleb = x

(1) Andy gives 1/4 of his ((1/4)x) to Ben:
Andy = (3/4)x
Ben = (5/4)x
Caleb = x

(2) Ben gives 2/5 of his to Caleb:
Andy = (3/4)x
Ben = (3/5)(5/4)x = (3/4)x
Caleb: x+(2/5)(5/4)x = (3/2)x

(3) Caleb gives 161 of his to charity:
Andy = (3/4)x
Ben = (3/4)x
Caleb = (3/2)x-161

At the end Caleb had 5/6 as many as Andy:

%283%2F2%29x-161+=+%285%2F6%29%283%2F4%29x+=+%285%2F8%29x
%283%2F2%29x-%285%2F8%29x=161
%287%2F8%29x=161
x=%288%2F7%29161=8%2823%29=184

Together at first the three boys has 3(184)=552 stamps.

ANSWER: 552