Elyse, Diana, Ivory and Tammy jointly contributed to the cost of a present for their brother. Elyse's contribution is ⁷₉ of the total contribution made by the four girls. The ratio of Tammy's contribution to the total of Diana's and Ivory's contribution is 3 : 1. What is the total contribution by the four girls if Diana's contribution is ¹₆ of Ivory's contribution and the total amount contributed by Elyse and Tammy is $714?

Elyse	Diana	Ivory	Tammy	Total
7x14	2x14			9x14
	1x7		3x7
	1x1	6x1
98 u	1 u	6 u	21 u	126 u

Working backwards.

Total amount that Diana and Ivory had is the combined repeated identity.
LCM of 1 and 7 = 7

Total amount that Diana, Ivory and Tammy had is the next combined repeated identity.
LCM of 2 and 14 = 28 

Total amount contributed by Elyse and Tammy
= 98 u + 21 u
= 119 u

119 u = 714

1 u = 714 ÷ 119 = $6

Total contribution by the four girls
= 126 u
= 126 x 6
= $756

Answer(s): $756