Winnie, Fiona, Shiyun and Kathy jointly contributed to the cost of a present for their brother. Winnie's contribution is ⁴₅ of the total contribution made by the four girls. The ratio of Kathy's contribution to the total of Fiona's and Shiyun's contribution is 2 : 1. What is the total contribution by the four girls if Fiona's contribution is ¹₄ of Shiyun's contribution and the total amount contributed by Winnie and Kathy is $350?

Winnie	Fiona	Shiyun	Kathy	Total
4x15	1x15			5x15
	1x5		2x5
	1x1	4x1
60 u	1 u	4 u	10 u	75 u

Working backwards.

Total amount that Fiona and Shiyun had is the combined repeated identity.
LCM of 1 and 5 = 5

Total amount that Fiona, Shiyun and Kathy had is the next combined repeated identity.
LCM of 1 and 15 = 15 

Total amount contributed by Winnie and Kathy
= 60 u + 10 u
= 70 u

70 u = 350

1 u = 350 ÷ 70 = $5

Total contribution by the four girls
= 75 u
= 75 x 5
= $375

Answer(s): $375