Sabrina, Tina, Xuan and Jane jointly contributed to the cost of a present for their sister. Sabrina's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Jane's contribution to the total of Tina's and Xuan's contribution is 5 : 2. What is the total contribution by the four girls if Tina's contribution is ²₃ of Xuan's contribution and the total amount contributed by Sabrina and Jane is $420?

Sabrina	Tina	Xuan	Jane	Total
1x35	1x35			2x35
	2x5		5x5
	2x2	3x2
35 u	4 u	6 u	25 u	70 u

Working backwards.

Total amount that Tina and Xuan had is the combined repeated identity.
LCM of 2 and 5 = 10

Total amount that Tina, Xuan and Jane had is the next combined repeated identity.
LCM of 1 and 35 = 35 

Total amount contributed by Sabrina and Jane
= 35 u + 25 u
= 60 u

60 u = 420

2 u = 420 ÷ 60 = $7

Total contribution by the four girls
= 70 u
= 70 x 7
= $490

Answer(s): $490