Vanessa, Tammy, Mary and Raeann jointly contributed to the cost of a present for their colleague. Vanessa's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Raeann's contribution to the total of Tammy's and Mary's contribution is 5 : 4. What is the total contribution by the four girls if Tammy's contribution is ¹₈ of Mary's contribution and the total amount contributed by Vanessa and Raeann is $1386?

Vanessa	Tammy	Mary	Raeann	Total
1x81	1x81			2x81
	4x9		5x9
	1x4	8x4
81 u	4 u	32 u	45 u	162 u

Working backwards.

Total amount that Tammy and Mary had is the combined repeated identity.
LCM of 4 and 9 = 36

Total amount that Tammy, Mary and Raeann had is the next combined repeated identity.
LCM of 1 and 81 = 81 

Total amount contributed by Vanessa and Raeann
= 81 u + 45 u
= 126 u

126 u = 1386

4 u = 1386 ÷ 126 = $11

Total contribution by the four girls
= 162 u
= 162 x 11
= $1782

Answer(s): $1782