Rachel, Lucy, Linda and Kathy received a sum of money. Rachel received ⁵₈ of the total amount of money Lucy, Linda and Kathy received. Lucy received ¹₃ of the total amount of money Linda and Kathy received. Linda received ¹₅ as much money as Kathy. If Lucy received $27 less than Rachel, find the total sum of money the 4 girls received.

Rachel	Lucy	Linda	Kathy	Total
5x1	8x1
	1x2	3x2
		1x1	5x1
5 u	2 u	1 u	5 u	13 u

The total amount that Linda and Kathy have is repeated.  Make the total amount that Linda and Kathy have the same.  LCM of 6 and 3 is 6.

The total amount that Lucy, Linda and Kathy have is repeated.  Make the total amount that Lucy, Linda and Kathy have the same. LCM of 4 and 8 is 8.

Amount that Lucy had less than Rachel
= 5 u - 2 u
= 3 u

3 u = 27

1 u = 27 ÷ 3 = 9

Total sum of money that 4 girls received
= 5 u + 2 u + 1 u + 5 u 
= 13 u
= 13 x 9
= $117

Answer(s): $117