Julie, Xylia, Kimberly and Usha jointly contributed to the cost of a present for their brother. Julie's contribution is ⁶₇ of the total contribution made by the four girls. The ratio of Usha's contribution to the total of Xylia's and Kimberly's contribution is 4 : 3. What is the total contribution by the four girls if Xylia's contribution is ¹₃ of Kimberly's contribution and the total amount contributed by Julie and Usha is $2024?

Julie	Xylia	Kimberly	Usha	Total
6x28	1x28			7x28
	3x4		4x4
	1x3	3x3
168 u	3 u	9 u	16 u	196 u

Working backwards.

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

Total amount that Xylia, Kimberly and Usha had is the next combined repeated identity.
LCM of 1 and 28 = 28 

Total amount contributed by Julie and Usha
= 168 u + 16 u
= 184 u

184 u = 2024

3 u = 2024 ÷ 184 = $11

Total contribution by the four girls
= 196 u
= 196 x 11
= $2156

Answer(s): $2156