Barbara, Usha, Victoria and Hazel received a sum of money. Barbara received ⁵₈ of the total amount of money Usha, Victoria and Hazel received. Usha received ¹₃ of the total amount of money Victoria and Hazel received. Victoria received ¹₅ as much money as Hazel. If Barbara received $52 more than Victoria, find the total sum of money the 4 girls received.

Barbara	Usha	Victoria	Hazel	Total
5x1	8x1
	1x2	3x2
		1x1	5x1
5 u	2 u	1 u	5 u	13 u

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

The total amount that Usha, Victoria and Hazel have is repeated.  Make the total amount that Usha, Victoria and Hazel have the same. LCM of 4 and 8 is 8.

Amount that Barbara had more than Victoria
= 5 u - 1 u
= 4 u

4 u = 52

1 u = 52 ÷ 4 = 13

Total sum of money that 4 girls received
= 5 u + 2 u + 1 u + 5 u 
= 13 u
= 13 x 13
= $169

Answer(s): $169