Barbara had some red buttons and brown buttons in 2 packets. In Packet C, the ratio of the number of red buttons to brown buttons was 10 : 7. In Packet D, the number of red buttons was 4 times the number of brown buttons. Barbara transferred ⁴₇ of the brown buttons from Packet C to Packet D. The number of buttons in Packet C became 182 and the ratio of the number of red buttons to brown buttons in Packet D became 8 : 9.

1. How many brown buttons were transferred from Packet C to Packet D?
2. What was the number of buttons in Packet D after the transfer?

	Packet C		Packet D
	Red	Brown	Red	Brown
Comparing red buttons and brown buttons at first	10 u	7 u	4x2 = 8 p	1x2 = 2 p
Before		7 u
Change		- 4 u		+ 4 u
After		3 u
Comparing red buttons and brown buttons in the end	10 u	3 u	8 p	9 p

(a)
Total number of buttons in the end for Packet C
= 10 u + 3 u
= 13 u

13 u = 182

1 u = 182 ÷ 13 = 14

Number of brown buttons that were transferred from Packet C to Packet D
= 4 u
= 4 x 14
= 56

(b)
The number of red buttons in Packet D remains unchanged.  Make the number of red buttons in Packet D the same.  LCM of 4 and 8 is 8. 

Increase in the number of brown buttons in Packet D
= 9 p - 2 p
= 7 p

7 p = 4 u
7 p = 56

1 p = 56 ÷ 7 = 8

Number of buttons in Packet D in the end
= 8 p + 9 p
= 17 p
= 17 x 8
= 136

Answer(s): (a) 56; (b) 136