Yen, Jane, Risa and Hilda jointly contributed to the cost of a present for their classmate. Yen's contribution is ³₄ of the total contribution made by the four girls. The ratio of Hilda's contribution to the total of Jane's and Risa's contribution is 5 : 4. What is the total contribution by the four girls if Jane's contribution is ¹₂ of Risa's contribution and the total amount contributed by Yen and Hilda is $576?

Yen	Jane	Risa	Hilda	Total
3x27	1x27			4x27
	4x3		5x3
	1x4	2x4
81 u	4 u	8 u	15 u	108 u

Working backwards.

Total amount that Jane and Risa had is the combined repeated identity.
LCM of 4 and 3 = 12

Total amount that Jane, Risa and Hilda had is the next combined repeated identity.
LCM of 1 and 27 = 27 

Total amount contributed by Yen and Hilda
= 81 u + 15 u
= 96 u

96 u = 576

4 u = 576 ÷ 96 = $6

Total contribution by the four girls
= 108 u
= 108 x 6
= $648

Answer(s): $648