Irene, Roshel, Natalie and Olivia jointly contributed to the cost of a present for their schoolmate. Irene's contribution is ⁴₅ of the total contribution made by the four girls. The ratio of Olivia's contribution to the total of Roshel's and Natalie's contribution is 5 : 2. What is the total contribution by the four girls if Roshel's contribution is ¹₃ of Natalie's contribution and the total amount contributed by Irene and Olivia is $792?

Irene	Roshel	Natalie	Olivia	Total
4x14	1x14			5x14
	2x2		5x2
	1x1	3x1
56 u	1 u	3 u	10 u	70 u

Working backwards.

Total amount that Roshel and Natalie had is the combined repeated identity.
LCM of 2 and 4 = 4

Total amount that Roshel, Natalie and Olivia had is the next combined repeated identity.
LCM of 1 and 14 = 14 

Total amount contributed by Irene and Olivia
= 56 u + 10 u
= 66 u

66 u = 792

2 u = 792 ÷ 66 = $12

Total contribution by the four girls
= 70 u
= 70 x 12
= $840

Answer(s): $840