Hilda, Emma, Roshel and Gillian jointly contributed to the cost of a present for their colleague. Hilda's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Gillian's contribution to the total of Emma's and Roshel's contribution is 3 : 1. What is the total contribution by the four girls if Emma's contribution is ¹₂ of Roshel's contribution and the total amount contributed by Hilda and Gillian is $315?

Hilda	Emma	Roshel	Gillian	Total
1x12	1x12			2x12
	1x3		3x3
	1x1	2x1
12 u	1 u	2 u	9 u	24 u

Working backwards.

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

Total amount that Emma, Roshel and Gillian had is the next combined repeated identity.
LCM of 1 and 12 = 12 

Total amount contributed by Hilda and Gillian
= 12 u + 9 u
= 21 u

21 u = 315

1 u = 315 ÷ 21 = $15

Total contribution by the four girls
= 24 u
= 24 x 15
= $360

Answer(s): $360