Barbara, Esther, Kimberly and Winnie jointly contributed to the cost of a present for their schoolmate. Barbara's contribution is ⁴₅ of the total contribution made by the four girls. The ratio of Winnie's contribution to the total of Esther's and Kimberly's contribution is 5 : 2. What is the total contribution by the four girls if Esther's contribution is ¹₈ of Kimberly's contribution and the total amount contributed by Barbara and Winnie is $2970?

Barbara	Esther	Kimberly	Winnie	Total
4x63	1x63			5x63
	2x9		5x9
	1x2	8x2
252 u	2 u	16 u	45 u	315 u

Working backwards.

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

Total amount that Esther, Kimberly and Winnie had is the next combined repeated identity.
LCM of 1 and 63 = 63 

Total amount contributed by Barbara and Winnie
= 252 u + 45 u
= 297 u

297 u = 2970

2 u = 2970 ÷ 297 = $10

Total contribution by the four girls
= 315 u
= 315 x 10
= $3150

Answer(s): $3150