Eugene and Frank had a total of 772 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?
+128475 If both have the same number at the end then each has (772/2) = 386
Let E be the number that Eugene started with and F what Frank started with
And F = 772 - E (1)
Eugene gives away (1/3) of his
And from Frank he gets (1/5) ( F + (1/3) E ] = (1/5) ( 772 -E + 1/3)E ) (2)
So at the end, what Eugene started with - what he gave away + what he got from Frank = 336
So
E - (1/3)E + (1/5) (772 - E + (1/3)E ] = 336
(2/3)E + 772/5 + (1/5)(-2/3)E = 336
(2/3)E - (2/15)E = 336 - 772/5
[ 8/15] E = 908 / 5
8E = 2724
E = 340.5 ?????
Are your numbers correct ??? (it's also possible that I made an error !!! )
https://web2.0calc.com/questions/question-corrected
here is the question that's edited
+23245 CPhill --
I got your answer ??? but a different number.
Number Eugene starts with: E
Number Frank starts with: F
Eugene gave away 1/3 of his stamps to Frank ...
Now Eugene has: (2/3)E
and Frank has: F + (1/3)E
Frank then gave 1/5 of his stamps to Eugene ...
Now Eugene has: (2/3)E + (1/5)( F + (1/3)E )
and Frank has: (4/5)( F + (1/3)E )
They now have the same number of stamps:
(2/3)E + (1/5)( F + (1/3)E ) = (4/5)( F + (1/3)E )
(2/3)E + (1/5)F + (1/15)E = (4/5)F + (4/15)E
multiply by 15: 10E + 3F + E = 12F + 4E
11E + 3F = 12F + 4E
7E = 9F
Since E + F = 772 ---> F = 772 - E
7E = 9(772 - E)
7E = 6948 - 9E
16E = 6948
E = 434.25
Final result: ?????
