Usha, Hilda and Cathy have equal number of cards. Usha packs all her cards equally into 4 packets. Hilda packs all her cards equally into 8 packets. Cathy packs all her cards equally into 10 packets. 3 packets of Usha's cards, 2 packets of Hilda's cards and 7 packets of Cathy's cards add up to 612 cards. How many cards do they have altogether?

	Usha	Hilda	Cathy
Number of packets	4	8	10
Number of cards	40 u	40 u	40 u
Number of cards in each packet	10 u	5 u	4 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, 8 and 10 = 40

Number of cards that each child has = 40 u

Number of cards in 1 packet of Usha's cards = 40 u ÷ 4 = 10 u
Number of cards in 1 packet of Hilda's cards = 40 u ÷ 8 = 5 u
Number of cards in 1 packet of Cathy's cards = 40 u ÷ 10 = 4 u

Number of cards in 3 packets of Usha's cards, 2 packets of Hilda's cards and 7 packets of Cathy's cards
= (3 x 10 u) + (2 x 5 u) + (7 x 4 u)
= 30 u + 10 u + 28 u
= 68 u

68 u = 612

1 u = 612 ÷ 68 = 9

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

Answer(s): 1080