Penelope, Jane, Rachel and Fanny jointly contributed to the cost of a present for their brother. Penelope's contribution is ³₄ of the total contribution made by the four girls. The ratio of Fanny's contribution to the total of Jane's and Rachel's contribution is 3 : 1. What is the total contribution by the four girls if Jane's contribution is ¹₅ of Rachel's contribution and the total amount contributed by Penelope and Fanny is $990?

Penelope	Jane	Rachel	Fanny	Total
3x24	1x24			4x24
	1x6		3x6
	1x1	5x1
72 u	1 u	5 u	18 u	96 u

Working backwards.

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

Total amount that Jane, Rachel and Fanny had is the next combined repeated identity.
LCM of 1 and 24 = 24 

Total amount contributed by Penelope and Fanny
= 72 u + 18 u
= 90 u

90 u = 990

1 u = 990 ÷ 90 = $11

Total contribution by the four girls
= 96 u
= 96 x 11
= $1056

Answer(s): $1056