Ivan, Wesley and Xavier have some buttons. The ratios of their buttons are as follows:

Ivan : (Ivan + Wesley + Xavier) = 1 : 4
Wesley : (Ivan + Xavier) = 1 : 4

Xavier has 21 buttons more than Wesley. In the end, Xavier gives away all he has to Wesley and Ivan so that both Wesley and Ivan end up with the same number of buttons, how many buttons has Ivan received from Xavier?

Wesley	Xavier	Ivan	Total
3x5		1x5	4x5
1x4	4x4		5x4
4 u	11 u	5 u	20 u

The total number of buttons is repeated.  Make the total number of buttons the same.  LCM of 4 and 5 is 20.

Number of buttons that Xavier has more than Wesley
= 11 u - 4 u
= 7 u

7 u = 21

1 u = 21 ÷ 7 = 3

	Wesley	Xavier	Ivan
Before	4 u	11 u	5 u
Change	+ 6 u	- 11 u	+ 5 u
After	10 u	0 u	10 u

Number of buttons that Ivan has received from Xavier
= 10 u - 5 u 
= 5 u
= 5 x 3
= 15

Answer(s): 15