Question 818563
belle and cally shared some buttons in the ratio 3:7.
 cally gave some buttons to belle such that they had an equal number of buttons in the end. 
if cally gave belle 16 buttons, how many buttons did belle have at the start?
:
Let x = "the multiplier"
then
3x =  b's original number of buttons
and
7x =  c's buttons
:
7x - 16 = 3x + 16
7x - 3x = 16 + 16
4x = 32
x = 32/4
x = 8 is the multiplier, therefore
8(3) = 24 buttons for b
and
8(7) = 56 buttons for c