Cathy, Opal and Kimberly have equal number of cards. Cathy packs all her cards equally into 8 packets. Opal packs all her cards equally into 10 packets. Kimberly packs all her cards equally into 5 packets. 5 packets of Cathy's cards, 3 packets of Opal's cards and 4 packets of Kimberly's cards add up to 552 cards. How many cards do they have altogether?

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

Number of cards that each child has = 40 u

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

Number of cards in 5 packets of Cathy's cards, 3 packets of Opal's cards and 4 packets of Kimberly's cards
= (5 x 5 u) + (3 x 4 u) + (4 x 8 u)
= 25 u + 12 u + 32 u
= 69 u

69 u = 552

1 u = 552 ÷ 69 = 8

Total number of cards that they have
= 3 x 40 u
= 120 u
= 120 x 8
= 960

Answer(s): 960