Esther, Abi, Zoe and Vanessa jointly contributed to the cost of a present for their classmate. Esther's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Vanessa's contribution to the total of Abi's and Zoe's contribution is 4 : 3. What is the total contribution by the four girls if Abi's contribution is ¹₆ of Zoe's contribution and the total amount contributed by Esther and Vanessa is $385?

Esther	Abi	Zoe	Vanessa	Total
1x49	1x49			2x49
	3x7		4x7
	1x3	6x3
49 u	3 u	18 u	28 u	98 u

Working backwards.

Total amount that Abi and Zoe had is the combined repeated identity.
LCM of 3 and 7 = 21

Total amount that Abi, Zoe and Vanessa had is the next combined repeated identity.
LCM of 1 and 49 = 49 

Total amount contributed by Esther and Vanessa
= 49 u + 28 u
= 77 u

77 u = 385

3 u = 385 ÷ 77 = $5

Total contribution by the four girls
= 98 u
= 98 x 5
= $490

Answer(s): $490