Emily, Cindy and Sarah had a total of 174 buttons. The ratio of Cindy's buttons to Sarah's buttons was at first 8 : 5. After Emily and Cindy each gave half of their buttons away, the 3 children had 112 buttons left. How many buttons did Emily and Cindy have at first?

	Emily	Cindy	Sarah	Total
Before	2 p	8 u	5 u	174
Change	- 1 p	- 4 u		- 62
After	1 p	4 u	5 u	112

Number of buttons that Emily and Cindy gave away
= 174 - 112
= 62

1 p + 4 u = 62
1 p = 62 - 4 u --- (1)

1 p + 4 u + 5 u = 112
1 p + 9 u = 112
1 p = 112 - 9 u --- (2)

(1) = (2)
62 - 4 u = 112 - 9 u
9 u - 4 u = 112 - 62
5 u = 50

1 u = 50 ÷ 5 = 10

From (1)
1 p = 62 - 4 u
1 p = 62 - 4 x 10

1 p = 62 - 40 = 22

Number of buttons that Emily and Cindy had at first
= 2 p + 8 u
= 2 x 22 + 8 x 10
= 44 + 50
= 94

Answer(s): 94