Abi, Lynn, Wendy and Penelope jointly contributed to the cost of a present for their sister. Abi's contribution is ⁸₉ of the total contribution made by the four girls. The ratio of Penelope's contribution to the total of Lynn's and Wendy's contribution is 4 : 1. What is the total contribution by the four girls if Lynn's contribution is ¹₃ of Wendy's contribution and the total amount contributed by Abi and Penelope is $2640?

Abi	Lynn	Wendy	Penelope	Total
8x20	1x20			9x20
	1x4		4x4
	1x1	3x1
160 u	1 u	3 u	16 u	180 u

Working backwards.

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

Total amount that Lynn, Wendy and Penelope had is the next combined repeated identity.
LCM of 1 and 20 = 20 

Total amount contributed by Abi and Penelope
= 160 u + 16 u
= 176 u

176 u = 2640

1 u = 2640 ÷ 176 = $15

Total contribution by the four girls
= 180 u
= 180 x 15
= $2700

Answer(s): $2700