Betty, Cathy, Gabby and Elyse jointly contributed to the cost of a present for their sister. Betty's contribution is ³₄ of the total contribution made by the four girls. The ratio of Elyse's contribution to the total of Cathy's and Gabby's contribution is 5 : 2. What is the total contribution by the four girls if Cathy's contribution is ¹₄ of Gabby's contribution and the total amount contributed by Betty and Elyse is $1560?

Betty	Cathy	Gabby	Elyse	Total
3x35	1x35			4x35
	2x5		5x5
	1x2	4x2
105 u	2 u	8 u	25 u	140 u

Working backwards.

Total amount that Cathy and Gabby had is the combined repeated identity.
LCM of 2 and 5 = 10

Total amount that Cathy, Gabby and Elyse had is the next combined repeated identity.
LCM of 1 and 35 = 35 

Total amount contributed by Betty and Elyse
= 105 u + 25 u
= 130 u

130 u = 1560

2 u = 1560 ÷ 130 = $12

Total contribution by the four girls
= 140 u
= 140 x 12
= $1680

Answer(s): $1680