Emily, Linda, Winnie and Joelle jointly contributed to the cost of a present for their classmate. Emily's contribution is ³₄ of the total contribution made by the four girls. The ratio of Joelle's contribution to the total of Linda's and Winnie's contribution is 5 : 2. What is the total contribution by the four girls if Linda's contribution is ¹₃ of Winnie's contribution and the total amount contributed by Emily and Joelle is $520?

Emily	Linda	Winnie	Joelle	Total
3x14	1x14			4x14
	2x2		5x2
	1x1	3x1
42 u	1 u	3 u	10 u	56 u

Working backwards.

Total amount that Linda and Winnie had is the combined repeated identity.
LCM of 2 and 4 = 4

Total amount that Linda, Winnie and Joelle had is the next combined repeated identity.
LCM of 1 and 14 = 14 

Total amount contributed by Emily and Joelle
= 42 u + 10 u
= 52 u

52 u = 520

2 u = 520 ÷ 52 = $10

Total contribution by the four girls
= 56 u
= 56 x 10
= $560

Answer(s): $560