Tammy, Kathy, Olivia and Usha jointly contributed to the cost of a present for their colleague. Tammy's contribution is ¹₄ of the total contribution made by the four girls. The ratio of Usha's contribution to the total of Kathy's and Olivia's contribution is 5 : 1. What is the total contribution by the four girls if Kathy's contribution is ¹₈ of Olivia's contribution and the total amount contributed by Tammy and Usha is $693?

Tammy	Kathy	Olivia	Usha	Total
1x18	3x18			4x18
	1x9		5x9
	1x1	8x1
18 u	1 u	8 u	45 u	72 u

Working backwards.

Total amount that Kathy and Olivia had is the combined repeated identity.
LCM of 1 and 9 = 9

Total amount that Kathy, Olivia and Usha had is the next combined repeated identity.
LCM of 3 and 18 = 54 

Total amount contributed by Tammy and Usha
= 18 u + 45 u
= 63 u

63 u = 693

1 u = 693 ÷ 63 = $11

Total contribution by the four girls
= 72 u
= 72 x 11
= $792

Answer(s): $792