Eugene and Frank had a total of 272 stamps. Eugene gave 1/3 of his stamps to Frank. Frank then gave 1/5 of his stamps to Eugene. In the end, each of them had the same number of stamps. How many stamps did Eugene have at first?

Guest Apr 18, 2022

#1**+1 **

If both have the same number at the end then each has (272/2) = 136

Let E be the number that Eugene started with and F what Frank started with

And F = 272 - E

Eugene gives away (1/3) of his

And from Frank he gets (1/5) ( F + (1/3) E ) = (1/5) ( 272 - E + (1/3)E ) (2)

So at the end, what Eugene started with - what he gave away + what he got from Frank = 136

So

E - (1/3)E + (1/5) [ (272 - E + (1/3)E ] = 136

(2/3)E + 272/5 + (1/5)(-2/3)E = 136

(2/3)E - (2/15)E = 136 - 272/5

[ 8/15] E = 408 / 5

8E = 1224

E = 153 = stamps that Eugene started with

And Frank started with 119

Proof

Eugene gives (1/3) to Frank = (153) / 3 = 51

Eugene now has 102

And now Frank has 119 + 51 = 170

He gives 1/5 of these to Eugene = 34

Eugene now has 102 + 34 = 136

Frank now has 119 + 51 - 34 = 136

CPhill Apr 18, 2022