Natalie, Fiona, Sarah and Gwen jointly contributed to the cost of a present for their classmate. Natalie's contribution is ³₇ of the total contribution made by the four girls. The ratio of Gwen's contribution to the total of Fiona's and Sarah's contribution is 5 : 3. What is the total contribution by the four girls if Fiona's contribution is ¹₅ of Sarah's contribution and the total amount contributed by Natalie and Gwen is $418?

Natalie	Fiona	Sarah	Gwen	Total
3x4	4x4			7x4
	3x2		5x2
	1x1	5x1
12 u	1 u	5 u	10 u	28 u

Working backwards.

Total amount that Fiona and Sarah had is the combined repeated identity.
LCM of 3 and 6 = 6

Total amount that Fiona, Sarah and Gwen had is the next combined repeated identity.
LCM of 4 and 4 = 16 

Total amount contributed by Natalie and Gwen
= 12 u + 10 u
= 22 u

22 u = 418

3 u = 418 ÷ 22 = $19

Total contribution by the four girls
= 28 u
= 28 x 19
= $532

Answer(s): $532