Shannon, Gillian, Shiyun and Yoko jointly contributed to the cost of a present for their sister. Shannon's contribution is ⁴₅ of the total contribution made by the four girls. The ratio of Yoko's contribution to the total of Gillian's and Shiyun's contribution is 2 : 1. What is the total contribution by the four girls if Gillian's contribution is ¹₃ of Shiyun's contribution and the total amount contributed by Shannon and Yoko is $616?

Shannon	Gillian	Shiyun	Yoko	Total
4x12	1x12			5x12
	1x4		2x4
	1x1	3x1
48 u	1 u	3 u	8 u	60 u

Working backwards.

Total amount that Gillian and Shiyun had is the combined repeated identity.
LCM of 1 and 4 = 4

Total amount that Gillian, Shiyun and Yoko had is the next combined repeated identity.
LCM of 1 and 12 = 12 

Total amount contributed by Shannon and Yoko
= 48 u + 8 u
= 56 u

56 u = 616

1 u = 616 ÷ 56 = $11

Total contribution by the four girls
= 60 u
= 60 x 11
= $660

Answer(s): $660