Shiyun, Rachel, Usha and Kylie jointly contributed to the cost of a present for their schoolmate. Shiyun's contribution is ¹₄ of the total contribution made by the four girls. The ratio of Kylie's contribution to the total of Rachel's and Usha's contribution is 4 : 3. What is the total contribution by the four girls if Rachel's contribution is ²₇ of Usha's contribution and the total amount contributed by Shiyun and Kylie is $342?

Shiyun	Rachel	Usha	Kylie	Total
1x7	3x7			4x7
	3x3		4x3
	2x1	7x1
7 u	2 u	7 u	12 u	28 u

Working backwards.

Total amount that Rachel and Usha had is the combined repeated identity.
LCM of 3 and 9 = 9

Total amount that Rachel, Usha and Kylie had is the next combined repeated identity.
LCM of 3 and 7 = 21 

Total amount contributed by Shiyun and Kylie
= 7 u + 12 u
= 19 u

19 u = 342

3 u = 342 ÷ 19 = $18

Total contribution by the four girls
= 28 u
= 28 x 18
= $504

Answer(s): $504