Gwen, Nora, Erika and Zoe jointly contributed to the cost of a present for their colleague. Gwen's contribution is ⁷₈ of the total contribution made by the four girls. The ratio of Zoe's contribution to the total of Nora's and Erika's contribution is 5 : 2. What is the total contribution by the four girls if Nora's contribution is ¹₄ of Erika's contribution and the total amount contributed by Gwen and Zoe is $4320?

Gwen	Nora	Erika	Zoe	Total
7x35	1x35			8x35
	2x5		5x5
	1x2	4x2
245 u	2 u	8 u	25 u	280 u

Working backwards.

Total amount that Nora and Erika had is the combined repeated identity.
LCM of 2 and 5 = 10

Total amount that Nora, Erika and Zoe had is the next combined repeated identity.
LCM of 1 and 35 = 35 

Total amount contributed by Gwen and Zoe
= 245 u + 25 u
= 270 u

270 u = 4320

2 u = 4320 ÷ 270 = $16

Total contribution by the four girls
= 280 u
= 280 x 16
= $4480

Answer(s): $4480