Zara, Shiyun, Sabrina and Jen jointly contributed to the cost of a present for their brother. Zara's contribution is ¹₅ of the total contribution made by the four girls. The ratio of Jen's contribution to the total of Shiyun's and Sabrina's contribution is 5 : 1. What is the total contribution by the four girls if Shiyun's contribution is ¹₃ of Sabrina's contribution and the total amount contributed by Zara and Jen is $312?

Zara	Shiyun	Sabrina	Jen	Total
1x6	4x6			5x6
	1x4		5x4
	1x1	3x1
6 u	1 u	3 u	20 u	30 u

Working backwards.

Total amount that Shiyun and Sabrina had is the combined repeated identity.
LCM of 1 and 4 = 4

Total amount that Shiyun, Sabrina and Jen had is the next combined repeated identity.
LCM of 4 and 6 = 24 

Total amount contributed by Zara and Jen
= 6 u + 20 u
= 26 u

26 u = 312

1 u = 312 ÷ 26 = $12

Total contribution by the four girls
= 30 u
= 30 x 12
= $360

Answer(s): $360