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?
+130071 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
