Marion, Mary and Xandra have equal number of cards. Marion packs all her cards equally into 4 packets. Mary packs all her cards equally into 10 packets. Xandra packs all her cards equally into 8 packets. 3 packets of Marion's cards, 5 packets of Mary's cards and 2 packets of Xandra's cards add up to 240 cards. How many cards do they have altogether?

	Marion	Mary	Xandra
Number of packets	4	10	8
Number of cards	40 u	40 u	40 u
Number of cards in each packet	10 u	4 u	5 u

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

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

Number of cards that each child has = 40 u

Number of cards in 1 packet of Marion's cards = 40 u ÷ 4 = 10 u
Number of cards in 1 packet of Mary's cards = 40 u ÷ 10 = 4 u
Number of cards in 1 packet of Xandra's cards = 40 u ÷ 8 = 5 u

Number of cards in 3 packets of Marion's cards, 5 packets of Mary's cards and 2 packets of Xandra's cards
= (3 x 10 u) + (5 x 4 u) + (2 x 5 u)
= 30 u + 20 u + 10 u
= 60 u

60 u = 240

1 u = 240 ÷ 60 = 4

Total number of cards that they have
= 3 x 40 u
= 120 u
= 120 x 4
= 480

Answer(s): 480