Dana, Shannon and Kathy have equal number of marbles. Dana packs all her marbles equally into 10 packets. Shannon packs all her marbles equally into 5 packets. Kathy packs all her marbles equally into 8 packets. 5 packets of Dana's marbles, 3 packets of Shannon's marbles and 2 packets of Kathy's marbles add up to 540 marbles. How many marbles do they have altogether?

	Dana	Shannon	Kathy
Number of packets	10	5	8
Number of marbles	40 u	40 u	40 u
Number of marbles in each packet	4 u	8 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 10, 5 and 8 = 40

Number of marbles that each child has = 40 u

Number of marbles in 1 packet of Dana's marbles = 40 u ÷ 10 = 4 u
Number of marbles in 1 packet of Shannon's marbles = 40 u ÷ 5 = 8 u
Number of marbles in 1 packet of Kathy's marbles = 40 u ÷ 8 = 5 u

Number of marbles in 5 packets of Dana's marbles, 3 packets of Shannon's marbles and 2 packets of Kathy's marbles
= (5 x 4 u) + (3 x 8 u) + (2 x 5 u)
= 20 u + 24 u + 10 u
= 54 u

54 u = 540

1 u = 540 ÷ 54 = 10

Total number of marbles that they have
= 3 x 40 u
= 120 u
= 120 x 10
= 1200

Answer(s): 1200