Penelope, Elyse, Esther and Diana jointly contributed to the cost of a present for their classmate. Penelope's contribution is ¹₈ of the total contribution made by the four girls. The ratio of Diana's contribution to the total of Elyse's and Esther's contribution is 5 : 2. What is the total contribution by the four girls if Elyse's contribution is ²₇ of Esther's contribution and the total amount contributed by Penelope and Diana is $162?

Penelope	Elyse	Esther	Diana	Total
1x9	7x9			8x9
	2x9		5x9
	2x2	7x2
9 u	4 u	14 u	45 u	72 u

Working backwards.

Total amount that Elyse and Esther had is the combined repeated identity.
LCM of 2 and 9 = 18

Total amount that Elyse, Esther and Diana had is the next combined repeated identity.
LCM of 7 and 9 = 63 

Total amount contributed by Penelope and Diana
= 9 u + 45 u
= 54 u

54 u = 162

2 u = 162 ÷ 54 = $3

Total contribution by the four girls
= 72 u
= 72 x 3
= $216

Answer(s): $216