Xandra, Gabby, Hazel and Yoko jointly contributed to the cost of a present for their colleague. Xandra's contribution is ¹₃ of the total contribution made by the four girls. The ratio of Yoko's contribution to the total of Gabby's and Hazel's contribution is 2 : 1. What is the total contribution by the four girls if Gabby's contribution is ¹₃ of Hazel's contribution and the total amount contributed by Xandra and Yoko is $182?

Xandra	Gabby	Hazel	Yoko	Total
1x6	2x6			3x6
	1x4		2x4
	1x1	3x1
6 u	1 u	3 u	8 u	18 u

Working backwards.

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

Total amount that Gabby, Hazel and Yoko had is the next combined repeated identity.
LCM of 2 and 6 = 12 

Total amount contributed by Xandra and Yoko
= 6 u + 8 u
= 14 u

14 u = 182

1 u = 182 ÷ 14 = $13

Total contribution by the four girls
= 18 u
= 18 x 13
= $234

Answer(s): $234