Usha, Nora and Tammy have equal number of cards. Usha packs all her cards equally into 9 packets. Nora packs all her cards equally into 6 packets. Tammy packs all her cards equally into 4 packets. 4 packets of Usha's cards, 5 packets of Nora's cards and 3 packets of Tammy's cards add up to 219 cards. How many cards do they have altogether?

	Usha	Nora	Tammy
Number of packets	9	6	4
Number of cards	36 u	36 u	36 u
Number of cards in each packet	4 u	6 u	9 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 9, 6 and 4 = 36

Number of cards that each child has = 36 u

Number of cards in 1 packet of Usha's cards = 36 u ÷ 9 = 4 u
Number of cards in 1 packet of Nora's cards = 36 u ÷ 6 = 6 u
Number of cards in 1 packet of Tammy's cards = 36 u ÷ 4 = 9 u

Number of cards in 4 packets of Usha's cards, 5 packets of Nora's cards and 3 packets of Tammy's cards
= (4 x 4 u) + (5 x 6 u) + (3 x 9 u)
= 16 u + 30 u + 27 u
= 73 u

73 u = 219

1 u = 219 ÷ 73 = 3

Total number of cards that they have
= 3 x 36 u
= 108 u
= 108 x 3
= 324

Answer(s): 324