Rachel, Zara and Gabby have equal number of cards. Rachel packs all her cards equally into 4 packets. Zara packs all her cards equally into 5 packets. Gabby packs all her cards equally into 8 packets. 3 packets of Rachel's cards, 2 packets of Zara's cards and 5 packets of Gabby's cards add up to 355 cards. How many cards do they have altogether?

	Rachel	Zara	Gabby
Number of packets	4	5	8
Number of cards	40 u	40 u	40 u
Number of cards in each packet	10 u	8 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, 5 and 8 = 40

Number of cards that each child has = 40 u

Number of cards in 1 packet of Rachel's cards = 40 u ÷ 4 = 10 u
Number of cards in 1 packet of Zara's cards = 40 u ÷ 5 = 8 u
Number of cards in 1 packet of Gabby's cards = 40 u ÷ 8 = 5 u

Number of cards in 3 packets of Rachel's cards, 2 packets of Zara's cards and 5 packets of Gabby's cards
= (3 x 10 u) + (2 x 8 u) + (5 x 5 u)
= 30 u + 16 u + 25 u
= 71 u

71 u = 355

1 u = 355 ÷ 71 = 5

Total number of cards that they have
= 3 x 40 u
= 120 u
= 120 x 5
= 600

Answer(s): 600