Caden and Jenson shared some buttons in the ratio of 3 : 7. After both each gave away 30 buttons to their cousin, the ratio of the number of buttons Caden had to the total number of buttons left was 1 : 5. How many buttons did the two boys have at first?

	Caden	Jenson	Difference
Before	3x3 = 9 u	7x3 = 21 u	4x3 = 12 u
Change	- 30	- 30
After	1x4 = 4 u	4x4 = 16 u	3x4 = 12 u

Number of buttons that Caden and Jenson each gave to their cousin is the same.

The difference in the number of buttons at first and in the end between Caden and Jenson remains unchanged.  Make the difference in the number of buttons the same.  LCM of 4 and 3 is 12.

Number of buttons that Caden gave to their cousin
= 9 u - 4 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

Number of buttons that the two boys had at first
= 9 u + 21 u
= 30 u
= 30 x 6
= 180

Answer(s): 180