Xuan, Opal and Tiffany have equal number of cards. Xuan packs all her cards equally into 5 packets. Opal packs all her cards equally into 8 packets. Tiffany packs all her cards equally into 10 packets. 2 packets of Xuan's cards, 6 packets of Opal's cards and 4 packets of Tiffany's cards add up to 434 cards. How many cards do they have altogether?

	Xuan	Opal	Tiffany
Number of packets	5	8	10
Number of cards	40 u	40 u	40 u
Number of cards in each packet	8 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 5, 8 and 10 = 40

Number of cards that each child has = 40 u

Number of cards in 1 packet of Xuan's cards = 40 u ÷ 5 = 8 u
Number of cards in 1 packet of Opal's cards = 40 u ÷ 8 = 5 u
Number of cards in 1 packet of Tiffany's cards = 40 u ÷ 10 = 4 u

Number of cards in 2 packets of Xuan's cards, 6 packets of Opal's cards and 4 packets of Tiffany's cards
= (2 x 8 u) + (6 x 5 u) + (4 x 4 u)
= 16 u + 30 u + 16 u
= 62 u

62 u = 434

1 u = 434 ÷ 62 = 7

Total number of cards that they have
= 3 x 40 u
= 120 u
= 120 x 7
= 840

Answer(s): 840