SOLUTION: 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

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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      Log On


   



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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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