Sarah, Risa and Natalie have equal number of cards. Sarah packs all her cards equally into 4 packets. Risa packs all her cards equally into 8 packets. Natalie packs all her cards equally into 6 packets. 3 packets of Sarah's cards, 2 packets of Risa's cards and 5 packets of Natalie's cards add up to 220 cards. How many cards do they have altogether?

	Sarah	Risa	Natalie
Number of packets	4	8	6
Number of cards	24 u	24 u	24 u
Number of cards in each packet	6 u	3 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 6 = 24

Number of cards that each child has = 24 u

Number of cards in 1 packet of Sarah's cards = 24 u ÷ 4 = 6 u
Number of cards in 1 packet of Risa's cards = 24 u ÷ 8 = 3 u
Number of cards in 1 packet of Natalie's cards = 24 u ÷ 6 = 4 u

Number of cards in 3 packets of Sarah's cards, 2 packets of Risa's cards and 5 packets of Natalie's cards
= (3 x 6 u) + (2 x 3 u) + (5 x 4 u)
= 18 u + 6 u + 20 u
= 44 u

44 u = 220

1 u = 220 ÷ 44 = 5

Total number of cards that they have
= 3 x 24 u
= 72 u
= 72 x 5
= 360

Answer(s): 360