Kathy, Yoko, Lynn and Fiona jointly contributed to the cost of a present for their brother. Kathy's contribution is ⁷₈ of the total contribution made by the four girls. The ratio of Fiona's contribution to the total of Yoko's and Lynn's contribution is 4 : 1. What is the total contribution by the four girls if Yoko's contribution is ²₅ of Lynn's contribution and the total amount contributed by Kathy and Fiona is $2184?

Kathy	Yoko	Lynn	Fiona	Total
7x35	1x35			8x35
	1x7		4x7
	2x1	5x1
245 u	2 u	5 u	28 u	280 u

Working backwards.

Total amount that Yoko and Lynn had is the combined repeated identity.
LCM of 1 and 7 = 7

Total amount that Yoko, Lynn and Fiona had is the next combined repeated identity.
LCM of 1 and 35 = 35 

Total amount contributed by Kathy and Fiona
= 245 u + 28 u
= 273 u

273 u = 2184

1 u = 2184 ÷ 273 = $8

Total contribution by the four girls
= 280 u
= 280 x 8
= $2240

Answer(s): $2240