Nicole, Sarah and Lucy had a total of 80 buttons. The ratio of Sarah's buttons to Lucy's buttons was at first 12 : 7. After Nicole and Sarah each gave half of their buttons away, the 3 children had 47 buttons left. How many buttons did Nicole and Sarah have at first?

	Nicole	Sarah	Lucy	Total
Before	2 p	12 u	7 u	80
Change	- 1 p	- 6 u		- 33
After	1 p	6 u	7 u	47

Number of buttons that Nicole and Sarah gave away
= 80 - 47
= 33

1 p + 6 u = 33
1 p = 33 - 6 u --- (1)

1 p + 6 u + 7 u = 47
1 p + 13 u = 47
1 p = 47 - 13 u --- (2)

(1) = (2)
33 - 6 u = 47 - 13 u
13 u - 6 u = 47 - 33
7 u = 14

1 u = 14 ÷ 7 = 2

From (1)
1 p = 33 - 6 u
1 p = 33 - 6 x 2

1 p = 33 - 12 = 21

Number of buttons that Nicole and Sarah had at first
= 2 p + 12 u
= 2 x 21 + 12 x 2
= 42 + 14
= 56

Answer(s): 56