Kylie, Shiyun, Eva and Hilda jointly contributed to the cost of a present for their sister. Kylie's contribution is ¹₄ of the total contribution made by the four girls. The ratio of Hilda's contribution to the total of Shiyun's and Eva's contribution is 4 : 1. What is the total contribution by the four girls if Shiyun's contribution is ¹₅ of Eva's contribution and the total amount contributed by Kylie and Hilda is $102?

Kylie	Shiyun	Eva	Hilda	Total
1x10	3x10			4x10
	1x6		4x6
	1x1	5x1
10 u	1 u	5 u	24 u	40 u

Working backwards.

Total amount that Shiyun and Eva had is the combined repeated identity.
LCM of 1 and 6 = 6

Total amount that Shiyun, Eva and Hilda had is the next combined repeated identity.
LCM of 3 and 10 = 30 

Total amount contributed by Kylie and Hilda
= 10 u + 24 u
= 34 u

34 u = 102

1 u = 102 ÷ 34 = $3

Total contribution by the four girls
= 40 u
= 40 x 3
= $120

Answer(s): $120