Hilda, Xandra, Natalie and Sarah jointly contributed to the cost of a present for their brother. Hilda's contribution is ³₄ of the total contribution made by the four girls. The ratio of Sarah's contribution to the total of Xandra's and Natalie's contribution is 3 : 1. What is the total contribution by the four girls if Xandra's contribution is ¹₃ of Natalie's contribution and the total amount contributed by Hilda and Sarah is $360?

Hilda	Xandra	Natalie	Sarah	Total
3x16	1x16			4x16
	1x4		3x4
	1x1	3x1
48 u	1 u	3 u	12 u	64 u

Working backwards.

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

Total amount that Xandra, Natalie and Sarah had is the next combined repeated identity.
LCM of 1 and 16 = 16 

Total amount contributed by Hilda and Sarah
= 48 u + 12 u
= 60 u

60 u = 360

1 u = 360 ÷ 60 = $6

Total contribution by the four girls
= 64 u
= 64 x 6
= $384

Answer(s): $384