Ivory, Xandra, Nicole and Fanny jointly contributed to the cost of a present for their classmate. Ivory's contribution is ²₃ of the total contribution made by the four girls. The ratio of Fanny's contribution to the total of Xandra's and Nicole's contribution is 2 : 1. What is the total contribution by the four girls if Xandra's contribution is ¹₃ of Nicole's contribution and the total amount contributed by Ivory and Fanny is $480?

Ivory	Xandra	Nicole	Fanny	Total
2x12	1x12			3x12
	1x4		2x4
	1x1	3x1
24 u	1 u	3 u	8 u	36 u

Working backwards.

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

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

Total amount contributed by Ivory and Fanny
= 24 u + 8 u
= 32 u

32 u = 480

1 u = 480 ÷ 32 = $15

Total contribution by the four girls
= 36 u
= 36 x 15
= $540

Answer(s): $540