Esther, Yoko, Kathy and Wendy jointly contributed to the cost of a present for their colleague. Esther's contribution is ³₄ of the total contribution made by the four girls. The ratio of Wendy's contribution to the total of Yoko's and Kathy's contribution is 3 : 2. What is the total contribution by the four girls if Yoko's contribution is ²₇ of Kathy's contribution and the total amount contributed by Esther and Wendy is $486?

Esther	Yoko	Kathy	Wendy	Total
3x45	1x45			4x45
	2x9		3x9
	2x2	7x2
135 u	4 u	14 u	27 u	180 u

Working backwards.

Total amount that Yoko and Kathy had is the combined repeated identity.
LCM of 2 and 9 = 18

Total amount that Yoko, Kathy and Wendy had is the next combined repeated identity.
LCM of 1 and 45 = 45 

Total amount contributed by Esther and Wendy
= 135 u + 27 u
= 162 u

162 u = 486

2 u = 486 ÷ 162 = $3

Total contribution by the four girls
= 180 u
= 180 x 3
= $540

Answer(s): $540