Yen, Sarah, Jade and Elyse jointly contributed to the cost of a present for their brother. Yen's contribution is ²₃ of the total contribution made by the four girls. The ratio of Elyse's contribution to the total of Sarah's and Jade's contribution is 5 : 2. What is the total contribution by the four girls if Sarah's contribution is ¹₃ of Jade's contribution and the total amount contributed by Yen and Elyse is $304?

Yen	Sarah	Jade	Elyse	Total
2x14	1x14			3x14
	2x2		5x2
	1x1	3x1
28 u	1 u	3 u	10 u	42 u

Working backwards.

Total amount that Sarah and Jade had is the combined repeated identity.
LCM of 2 and 4 = 4

Total amount that Sarah, Jade and Elyse had is the next combined repeated identity.
LCM of 1 and 14 = 14 

Total amount contributed by Yen and Elyse
= 28 u + 10 u
= 38 u

38 u = 304

2 u = 304 ÷ 38 = $8

Total contribution by the four girls
= 42 u
= 42 x 8
= $336

Answer(s): $336