Julie, Natalie, Nora and Gillian jointly contributed to the cost of a present for their classmate. Julie's contribution is ²₃ of the total contribution made by the four girls. The ratio of Gillian's contribution to the total of Natalie's and Nora's contribution is 2 : 1. What is the total contribution by the four girls if Natalie's contribution is ¹₂ of Nora's contribution and the total amount contributed by Julie and Gillian is $456?

Julie	Natalie	Nora	Gillian	Total
2x9	1x9			3x9
	1x3		2x3
	1x1	2x1
18 u	1 u	2 u	6 u	27 u

Working backwards.

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

Total amount that Natalie, Nora and Gillian had is the next combined repeated identity.
LCM of 1 and 9 = 9 

Total amount contributed by Julie and Gillian
= 18 u + 6 u
= 24 u

24 u = 456

1 u = 456 ÷ 24 = $19

Total contribution by the four girls
= 27 u
= 27 x 19
= $513

Answer(s): $513