Emma, Gwen, Joelle and Dana received a sum of money. Emma received ²₅ of the total amount of money Gwen, Joelle and Dana received. Gwen received ¹₃ of the total amount of money Joelle and Dana received. Joelle received ¹₄ as much money as Dana. If Gwen received $30 less than Emma, find the total sum of money the 4 girls received.

Emma	Gwen	Joelle	Dana	Total
2x4	5x4
	1x5	3x5
		1x3	4x3
8 u	5 u	3 u	12 u	28 u

The total amount that Joelle and Dana have is repeated.  Make the total amount that Joelle and Dana have the same.  LCM of 5 and 3 is 15.

The total amount that Gwen, Joelle and Dana have is repeated.  Make the total amount that Gwen, Joelle and Dana have the same. LCM of 4 and 5 is 20.

Amount that Gwen had less than Emma
= 8 u - 5 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Total sum of money that 4 girls received
= 8 u + 5 u + 3 u + 12 u 
= 28 u
= 28 x 10
= $280

Answer(s): $280