Lucy, Tammy, Anna and Tina jointly contributed to the cost of a present for their sister. Lucy's contribution is ⁵₈ of the total contribution made by the four girls. The ratio of Tina's contribution to the total of Tammy's and Anna's contribution is 2 : 1. What is the total contribution by the four girls if Tammy's contribution is ¹₂ of Anna's contribution and the total amount contributed by Lucy and Tina is $84?

Lucy	Tammy	Anna	Tina	Total
5x3	3x3			8x3
	1x3		2x3
	1x1	2x1
15 u	1 u	2 u	6 u	24 u

Working backwards.

Total amount that Tammy and Anna had is the combined repeated identity.
LCM of 1 and 3 = 3

Total amount that Tammy, Anna and Tina had is the next combined repeated identity.
LCM of 3 and 3 = 9 

Total amount contributed by Lucy and Tina
= 15 u + 6 u
= 21 u

21 u = 84

1 u = 84 ÷ 21 = $4

Total contribution by the four girls
= 24 u
= 24 x 4
= $96

Answer(s): $96