Tina, Olivia and Gabby have equal number of cards. Tina packs all her cards equally into 6 packets. Olivia packs all her cards equally into 5 packets. Gabby packs all her cards equally into 10 packets. 3 packets of Tina's cards, 2 packets of Olivia's cards and 4 packets of Gabby's cards add up to 195 cards. How many cards do they have altogether?

	Tina	Olivia	Gabby
Number of packets	6	5	10
Number of cards	30 u	30 u	30 u
Number of cards in each packet	5 u	6 u	3 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 6, 5 and 10 = 30

Number of cards that each child has = 30 u

Number of cards in 1 packet of Tina's cards = 30 u ÷ 6 = 5 u
Number of cards in 1 packet of Olivia's cards = 30 u ÷ 5 = 6 u
Number of cards in 1 packet of Gabby's cards = 30 u ÷ 10 = 3 u

Number of cards in 3 packets of Tina's cards, 2 packets of Olivia's cards and 4 packets of Gabby's cards
= (3 x 5 u) + (2 x 6 u) + (4 x 3 u)
= 15 u + 12 u + 12 u
= 39 u

39 u = 195

1 u = 195 ÷ 39 = 5

Total number of cards that they have
= 3 x 30 u
= 90 u
= 90 x 5
= 450

Answer(s): 450