Cathy, Shannon, Lucy and Mary jointly contributed to the cost of a present for their sister. Cathy's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Mary's contribution to the total of Shannon's and Lucy's contribution is 3 : 2. What is the total contribution by the four girls if Shannon's contribution is ¹₅ of Lucy's contribution and the total amount contributed by Cathy and Mary is $312?

Cathy	Shannon	Lucy	Mary	Total
1x15	1x15			2x15
	2x3		3x3
	1x1	5x1
15 u	1 u	5 u	9 u	30 u

Working backwards.

Total amount that Shannon and Lucy had is the combined repeated identity.
LCM of 2 and 6 = 6

Total amount that Shannon, Lucy and Mary had is the next combined repeated identity.
LCM of 1 and 15 = 15 

Total amount contributed by Cathy and Mary
= 15 u + 9 u
= 24 u

24 u = 312

2 u = 312 ÷ 24 = $13

Total contribution by the four girls
= 30 u
= 30 x 13
= $390

Answer(s): $390