Anna, Lynn, Vanessa and Dana jointly contributed to the cost of a present for their classmate. Anna's contribution is ¹₅ of the total contribution made by the four girls. The ratio of Dana's contribution to the total of Lynn's and Vanessa's contribution is 3 : 1. What is the total contribution by the four girls if Lynn's contribution is ¹₈ of Vanessa's contribution and the total amount contributed by Anna and Dana is $396?

Anna	Lynn	Vanessa	Dana	Total
1x9	4x9			5x9
	1x9		3x9
	1x1	8x1
9 u	1 u	8 u	27 u	45 u

Working backwards.

Total amount that Lynn and Vanessa had is the combined repeated identity.
LCM of 1 and 9 = 9

Total amount that Lynn, Vanessa and Dana had is the next combined repeated identity.
LCM of 4 and 9 = 36 

Total amount contributed by Anna and Dana
= 9 u + 27 u
= 36 u

36 u = 396

1 u = 396 ÷ 36 = $11

Total contribution by the four girls
= 45 u
= 45 x 11
= $495

Answer(s): $495