Penelope, Joelle, Winnie and Betty jointly contributed to the cost of a present for their sister. Penelope's contribution is ⁸₉ of the total contribution made by the four girls. The ratio of Betty's contribution to the total of Joelle's and Winnie's contribution is 3 : 1. What is the total contribution by the four girls if Joelle's contribution is ¹₃ of Winnie's contribution and the total amount contributed by Penelope and Betty is $2380?

Penelope	Joelle	Winnie	Betty	Total
8x16	1x16			9x16
	1x4		3x4
	1x1	3x1
128 u	1 u	3 u	12 u	144 u

Working backwards.

Total amount that Joelle and Winnie had is the combined repeated identity.
LCM of 1 and 4 = 4

Total amount that Joelle, Winnie and Betty had is the next combined repeated identity.
LCM of 1 and 16 = 16 

Total amount contributed by Penelope and Betty
= 128 u + 12 u
= 140 u

140 u = 2380

1 u = 2380 ÷ 140 = $17

Total contribution by the four girls
= 144 u
= 144 x 17
= $2448

Answer(s): $2448