Opal, Diana, Lynn and Xylia jointly contributed to the cost of a present for their schoolmate. Opal's contribution is ⁵₈ of the total contribution made by the four girls. The ratio of Xylia's contribution to the total of Diana's and Lynn's contribution is 2 : 1. What is the total contribution by the four girls if Diana's contribution is ¹₃ of Lynn's contribution and the total amount contributed by Opal and Xylia is $448?

Opal	Diana	Lynn	Xylia	Total
5x4	3x4			8x4
	1x4		2x4
	1x1	3x1
20 u	1 u	3 u	8 u	32 u

Working backwards.

Total amount that Diana and Lynn had is the combined repeated identity.
LCM of 1 and 4 = 4

Total amount that Diana, Lynn and Xylia had is the next combined repeated identity.
LCM of 3 and 4 = 12 

Total amount contributed by Opal and Xylia
= 20 u + 8 u
= 28 u

28 u = 448

1 u = 448 ÷ 28 = $16

Total contribution by the four girls
= 32 u
= 32 x 16
= $512

Answer(s): $512