Raeann, Opal, Lynn and Esther jointly contributed to the cost of a present for their schoolmate. Raeann's contribution is ³₈ of the total contribution made by the four girls. The ratio of Esther's contribution to the total of Opal's and Lynn's contribution is 3 : 1. What is the total contribution by the four girls if Opal's contribution is ¹₄ of Lynn's contribution and the total amount contributed by Raeann and Esther is $162?

Raeann	Opal	Lynn	Esther	Total
3x4	5x4			8x4
	1x5		3x5
	1x1	4x1
12 u	1 u	4 u	15 u	32 u

Working backwards.

Total amount that Opal and Lynn had is the combined repeated identity.
LCM of 1 and 5 = 5

Total amount that Opal, Lynn and Esther had is the next combined repeated identity.
LCM of 5 and 4 = 20 

Total amount contributed by Raeann and Esther
= 12 u + 15 u
= 27 u

27 u = 162

1 u = 162 ÷ 27 = $6

Total contribution by the four girls
= 32 u
= 32 x 6
= $192

Answer(s): $192