Gwen, Natalie, Hilda and Ivory jointly contributed to the cost of a present for their sister. Gwen's contribution is ⁷₈ of the total contribution made by the four girls. The ratio of Ivory's contribution to the total of Natalie's and Hilda's contribution is 5 : 4. What is the total contribution by the four girls if Natalie's contribution is ¹₅ of Hilda's contribution and the total amount contributed by Gwen and Ivory is $2040?

Gwen	Natalie	Hilda	Ivory	Total
7x27	1x27			8x27
	4x3		5x3
	1x2	5x2
189 u	2 u	10 u	15 u	216 u

Working backwards.

Total amount that Natalie and Hilda had is the combined repeated identity.
LCM of 4 and 6 = 12

Total amount that Natalie, Hilda and Ivory had is the next combined repeated identity.
LCM of 1 and 27 = 27 

Total amount contributed by Gwen and Ivory
= 189 u + 15 u
= 204 u

204 u = 2040

4 u = 2040 ÷ 204 = $10

Total contribution by the four girls
= 216 u
= 216 x 10
= $2160

Answer(s): $2160