Jade, Usha, Gwen and Jane jointly contributed to the cost of a present for their sister. Jade's contribution is ⁴₇ of the total contribution made by the four girls. The ratio of Jane's contribution to the total of Usha's and Gwen's contribution is 2 : 1. What is the total contribution by the four girls if Usha's contribution is ¹₄ of Gwen's contribution and the total amount contributed by Jade and Jane is $270?

Jade	Usha	Gwen	Jane	Total
4x5	3x5			7x5
	1x5		2x5
	1x1	4x1
20 u	1 u	4 u	10 u	35 u

Working backwards.

Total amount that Usha and Gwen had is the combined repeated identity.
LCM of 1 and 5 = 5

Total amount that Usha, Gwen and Jane had is the next combined repeated identity.
LCM of 3 and 5 = 15 

Total amount contributed by Jade and Jane
= 20 u + 10 u
= 30 u

30 u = 270

1 u = 270 ÷ 30 = $9

Total contribution by the four girls
= 35 u
= 35 x 9
= $315

Answer(s): $315