Natalie, Shiyun, Jean and Tina jointly contributed to the cost of a present for their sister. Natalie's contribution is ³₄ of the total contribution made by the four girls. The ratio of Tina's contribution to the total of Shiyun's and Jean's contribution is 5 : 3. What is the total contribution by the four girls if Shiyun's contribution is ¹₃ of Jean's contribution and the total amount contributed by Natalie and Tina is $1160?

Natalie	Shiyun	Jean	Tina	Total
3x32	1x32			4x32
	3x4		5x4
	1x3	3x3
96 u	3 u	9 u	20 u	128 u

Working backwards.

Total amount that Shiyun and Jean had is the combined repeated identity.
LCM of 3 and 4 = 12

Total amount that Shiyun, Jean and Tina had is the next combined repeated identity.
LCM of 1 and 32 = 32 

Total amount contributed by Natalie and Tina
= 96 u + 20 u
= 116 u

116 u = 1160

3 u = 1160 ÷ 116 = $10

Total contribution by the four girls
= 128 u
= 128 x 10
= $1280

Answer(s): $1280