Natalie, Min and Jane have equal number of cards. Natalie packs all her cards equally into 4 packets. Min packs all her cards equally into 8 packets. Jane packs all her cards equally into 10 packets. 3 packets of Natalie's cards, 7 packets of Min's cards and 8 packets of Jane's cards add up to 970 cards. How many cards do they have altogether?

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

Number of cards that each child has = 40 u

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

Number of cards in 3 packets of Natalie's cards, 7 packets of Min's cards and 8 packets of Jane's cards
= (3 x 10 u) + (7 x 5 u) + (8 x 4 u)
= 30 u + 35 u + 32 u
= 97 u

97 u = 970

1 u = 970 ÷ 97 = 10

Total number of cards that they have
= 3 x 40 u
= 120 u
= 120 x 10
= 1200

Answer(s): 1200