Xylia, Erika, Gillian and Penelope received a sum of money. Xylia received ⁵₈ of the total amount of money Erika, Gillian and Penelope received. Erika received ¹₅ of the total amount of money Gillian and Penelope received. Gillian received ¹₃ as much money as Penelope. If Xylia received $110 more than Gillian, find the total sum of money the 4 girls received.

Xylia	Erika	Gillian	Penelope	Total
5x3	8x3
	1x4	5x4
		1x5	3x5
15 u	4 u	5 u	15 u	39 u

The total amount that Gillian and Penelope have is repeated.  Make the total amount that Gillian and Penelope have the same.  LCM of 4 and 5 is 20.

The total amount that Erika, Gillian and Penelope have is repeated.  Make the total amount that Erika, Gillian and Penelope have the same. LCM of 6 and 8 is 24.

Amount that Xylia had more than Gillian
= 15 u - 5 u
= 10 u

10 u = 110

1 u = 110 ÷ 10 = 11

Total sum of money that 4 girls received
= 15 u + 4 u + 5 u + 15 u 
= 39 u
= 39 x 11
= $429

Answer(s): $429