Winnie, Betty, Gem and Opal jointly contributed to the cost of a present for their schoolmate. Winnie's contribution is ¹₅ of the total contribution made by the four girls. The ratio of Opal's contribution to the total of Betty's and Gem's contribution is 5 : 3. What is the total contribution by the four girls if Betty's contribution is ²₃ of Gem's contribution and the total amount contributed by Winnie and Opal is $70?

Winnie	Betty	Gem	Opal	Total
1x10	4x10			5x10
	3x5		5x5
	2x3	3x3
10 u	6 u	9 u	25 u	50 u

Working backwards.

Total amount that Betty and Gem had is the combined repeated identity.
LCM of 3 and 5 = 15

Total amount that Betty, Gem and Opal had is the next combined repeated identity.
LCM of 4 and 10 = 40 

Total amount contributed by Winnie and Opal
= 10 u + 25 u
= 35 u

35 u = 70

3 u = 70 ÷ 35 = $2

Total contribution by the four girls
= 50 u
= 50 x 2
= $100

Answer(s): $100