Victoria, Gem and Xandra have equal number of cards. Victoria packs all her cards equally into 4 packets. Gem packs all her cards equally into 6 packets. Xandra packs all her cards equally into 9 packets. 3 packets of Victoria's cards, 2 packets of Gem's cards and 7 packets of Xandra's cards add up to 402 cards. How many cards do they have altogether?
| |
Victoria |
Gem |
Xandra |
| Number of packets |
4 |
6 |
9 |
| Number of cards |
36 u |
36 u |
36 u |
| Number of cards in each packet |
9 u |
6 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, 6 and 9 = 36
Number of cards that each child has = 36 u
Number of cards in 1 packet of Victoria's cards = 36 u ÷ 4 = 9 u
Number of cards in 1 packet of Gem's cards = 36 u ÷ 6 = 6 u
Number of cards in 1 packet of Xandra's cards = 36 u ÷ 9 = 4 u
Number of cards in 3 packets of Victoria's cards, 2 packets of Gem's cards and 7 packets of Xandra's cards
= (3 x 9 u) + (2 x 6 u) + (7 x 4 u)
= 27 u + 12 u + 28 u
= 67 u
67 u = 402
1 u = 402 ÷ 67 = 6
Total number of cards that they have
= 3 x 36 u
= 108 u
= 108 x 6
= 648
Answer(s): 648
