Xylia, Gabby, Nora and Raeann jointly contributed to the cost of a present for their schoolmate. Xylia's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Raeann's contribution to the total of Gabby's and Nora's contribution is 3 : 1. What is the total contribution by the four girls if Gabby's contribution is ¹₆ of Nora's contribution and the total amount contributed by Xylia and Raeann is $490?

Xylia	Gabby	Nora	Raeann	Total
1x28	1x28			2x28
	1x7		3x7
	1x1	6x1
28 u	1 u	6 u	21 u	56 u

Working backwards.

Total amount that Gabby and Nora had is the combined repeated identity.
LCM of 1 and 7 = 7

Total amount that Gabby, Nora and Raeann had is the next combined repeated identity.
LCM of 1 and 28 = 28 

Total amount contributed by Xylia and Raeann
= 28 u + 21 u
= 49 u

49 u = 490

1 u = 490 ÷ 49 = $10

Total contribution by the four girls
= 56 u
= 56 x 10
= $560

Answer(s): $560