Shiyun, Xandra, Jade and Rachel jointly contributed to the cost of a present for their schoolmate. Shiyun's contribution is ²₃ of the total contribution made by the four girls. The ratio of Rachel's contribution to the total of Xandra's and Jade's contribution is 3 : 1. What is the total contribution by the four girls if Xandra's contribution is ¹₂ of Jade's contribution and the total amount contributed by Shiyun and Rachel is $264?

Shiyun	Xandra	Jade	Rachel	Total
2x12	1x12			3x12
	1x3		3x3
	1x1	2x1
24 u	1 u	2 u	9 u	36 u

Working backwards.

Total amount that Xandra and Jade had is the combined repeated identity.
LCM of 1 and 3 = 3

Total amount that Xandra, Jade and Rachel had is the next combined repeated identity.
LCM of 1 and 12 = 12 

Total amount contributed by Shiyun and Rachel
= 24 u + 9 u
= 33 u

33 u = 264

1 u = 264 ÷ 33 = $8

Total contribution by the four girls
= 36 u
= 36 x 8
= $288

Answer(s): $288