Victoria, Irene and Olivia have equal number of marbles. Victoria packs all her marbles equally into 4 packets. Irene packs all her marbles equally into 10 packets. Olivia packs all her marbles equally into 8 packets. 2 packets of Victoria's marbles, 6 packets of Irene's marbles and 4 packets of Olivia's marbles add up to 576 marbles. How many marbles do they have altogether?

	Victoria	Irene	Olivia
Number of packets	4	10	8
Number of marbles	40 u	40 u	40 u
Number of marbles in each packet	10 u	4 u	5 u

All the marbles can be put into the packets without remainder.

All the children have equal numbers of marbles. 
Make the number of marbles that each child has the same. LCM of 4, 10 and 8 = 40

Number of marbles that each child has = 40 u

Number of marbles in 1 packet of Victoria's marbles = 40 u ÷ 4 = 10 u
Number of marbles in 1 packet of Irene's marbles = 40 u ÷ 10 = 4 u
Number of marbles in 1 packet of Olivia's marbles = 40 u ÷ 8 = 5 u

Number of marbles in 2 packets of Victoria's marbles, 6 packets of Irene's marbles and 4 packets of Olivia's marbles
= (2 x 10 u) + (6 x 4 u) + (4 x 5 u)
= 20 u + 24 u + 20 u
= 64 u

64 u = 576

1 u = 576 ÷ 64 = 9

Total number of marbles that they have
= 3 x 40 u
= 120 u
= 120 x 9
= 1080

Answer(s): 1080