Tina, Xylia, Elyse and Opal jointly contributed to the cost of a present for their classmate. Tina's contribution is ⁹₁₀ of the total contribution made by the four girls. The ratio of Opal's contribution to the total of Xylia's and Elyse's contribution is 4 : 3. What is the total contribution by the four girls if Xylia's contribution is ¹₆ of Elyse's contribution and the total amount contributed by Tina and Opal is $4690?

Tina	Xylia	Elyse	Opal	Total
9x49	1x49			10x49
	3x7		4x7
	1x3	6x3
441 u	3 u	18 u	28 u	490 u

Working backwards.

Total amount that Xylia and Elyse had is the combined repeated identity.
LCM of 3 and 7 = 21

Total amount that Xylia, Elyse and Opal had is the next combined repeated identity.
LCM of 1 and 49 = 49 

Total amount contributed by Tina and Opal
= 441 u + 28 u
= 469 u

469 u = 4690

3 u = 4690 ÷ 469 = $10

Total contribution by the four girls
= 490 u
= 490 x 10
= $4900

Answer(s): $4900