Jane, Diana, Shiyun and Hilda received a sum of money. Jane received ⁵₈ of the total amount of money Diana, Shiyun and Hilda received. Diana received ¹₅ of the total amount of money Shiyun and Hilda received. Shiyun received ¹₃ as much money as Hilda. If Diana received $121 less than Jane, find the total sum of money the 4 girls received.

Jane	Diana	Shiyun	Hilda	Total
5x3	8x3
	1x4	5x4
		1x5	3x5
15 u	4 u	5 u	15 u	39 u

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

The total amount that Diana, Shiyun and Hilda have is repeated.  Make the total amount that Diana, Shiyun and Hilda have the same. LCM of 6 and 8 is 24.

Amount that Diana had less than Jane
= 15 u - 4 u
= 11 u

11 u = 121

1 u = 121 ÷ 11 = 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