Gwen, Pamela, Erika and Nicole jointly contributed to the cost of a present for their brother. Gwen's contribution is ⁷₈ of the total contribution made by the four girls. The ratio of Nicole's contribution to the total of Pamela's and Erika's contribution is 5 : 3. What is the total contribution by the four girls if Pamela's contribution is ¹₇ of Erika's contribution and the total amount contributed by Gwen and Nicole is $9760?

Gwen	Pamela	Erika	Nicole	Total
7x64	1x64			8x64
	3x8		5x8
	1x3	7x3
448 u	3 u	21 u	40 u	512 u

Working backwards.

Total amount that Pamela and Erika had is the combined repeated identity.
LCM of 3 and 8 = 24

Total amount that Pamela, Erika and Nicole had is the next combined repeated identity.
LCM of 1 and 64 = 64 

Total amount contributed by Gwen and Nicole
= 448 u + 40 u
= 488 u

488 u = 9760

3 u = 9760 ÷ 488 = $20

Total contribution by the four girls
= 512 u
= 512 x 20
= $10240

Answer(s): $10240