Kathy, Usha, Tiffany and Cathy jointly contributed to the cost of a present for their brother. Kathy's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Cathy's contribution to the total of Usha's and Tiffany's contribution is 4 : 3. What is the total contribution by the four girls if Usha's contribution is ¹₇ of Tiffany's contribution and the total amount contributed by Kathy and Cathy is $1320?

Kathy	Usha	Tiffany	Cathy	Total
1x56	1x56			2x56
	3x8		4x8
	1x3	7x3
56 u	3 u	21 u	32 u	112 u

Working backwards.

Total amount that Usha and Tiffany had is the combined repeated identity.
LCM of 3 and 8 = 24

Total amount that Usha, Tiffany and Cathy had is the next combined repeated identity.
LCM of 1 and 56 = 56 

Total amount contributed by Kathy and Cathy
= 56 u + 32 u
= 88 u

88 u = 1320

3 u = 1320 ÷ 88 = $15

Total contribution by the four girls
= 112 u
= 112 x 15
= $1680

Answer(s): $1680