Marion, Jane and Lynn have equal number of cards. Marion packs all her cards equally into 10 packets. Jane packs all her cards equally into 4 packets. Lynn packs all her cards equally into 8 packets. 8 packets of Marion's cards, 2 packets of Jane's cards and 5 packets of Lynn's cards add up to 154 cards. How many cards do they have altogether?

	Marion	Jane	Lynn
Number of packets	10	4	8
Number of cards	40 u	40 u	40 u
Number of cards in each packet	4 u	10 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 10, 4 and 8 = 40

Number of cards that each child has = 40 u

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

Number of cards in 8 packets of Marion's cards, 2 packets of Jane's cards and 5 packets of Lynn's cards
= (8 x 4 u) + (2 x 10 u) + (5 x 5 u)
= 32 u + 20 u + 25 u
= 77 u

77 u = 154

1 u = 154 ÷ 77 = 2

Total number of cards that they have
= 3 x 40 u
= 120 u
= 120 x 2
= 240

Answer(s): 240