Usha, Dana, Sarah and Shannon jointly contributed to the cost of a present for their schoolmate. Usha's contribution is ³₄ of the total contribution made by the four girls. The ratio of Shannon's contribution to the total of Dana's and Sarah's contribution is 4 : 1. What is the total contribution by the four girls if Dana's contribution is ¹₃ of Sarah's contribution and the total amount contributed by Usha and Shannon is $152?

Usha	Dana	Sarah	Shannon	Total
3x20	1x20			4x20
	1x4		4x4
	1x1	3x1
60 u	1 u	3 u	16 u	80 u

Working backwards.

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

Total amount that Dana, Sarah and Shannon had is the next combined repeated identity.
LCM of 1 and 20 = 20 

Total amount contributed by Usha and Shannon
= 60 u + 16 u
= 76 u

76 u = 152

1 u = 152 ÷ 76 = $2

Total contribution by the four girls
= 80 u
= 80 x 2
= $160

Answer(s): $160