Barbara, Raeann, Min and Anna jointly contributed to the cost of a present for their schoolmate. Barbara's contribution is ¹₁₀ of the total contribution made by the four girls. The ratio of Anna's contribution to the total of Raeann's and Min's contribution is 2 : 1. What is the total contribution by the four girls if Raeann's contribution is ²₇ of Min's contribution and the total amount contributed by Barbara and Anna is $420?

Barbara	Raeann	Min	Anna	Total
1x3	9x3			10x3
	1x9		2x9
	2x1	7x1
3 u	2 u	7 u	18 u	30 u

Working backwards.

Total amount that Raeann and Min had is the combined repeated identity.
LCM of 1 and 9 = 9

Total amount that Raeann, Min and Anna had is the next combined repeated identity.
LCM of 9 and 3 = 27 

Total amount contributed by Barbara and Anna
= 3 u + 18 u
= 21 u

21 u = 420

1 u = 420 ÷ 21 = $20

Total contribution by the four girls
= 30 u
= 30 x 20
= $600

Answer(s): $600