Zara, Raeann and Victoria have equal number of cards. Zara packs all her cards equally into 9 packets. Raeann packs all her cards equally into 4 packets. Victoria packs all her cards equally into 6 packets. 7 packets of Zara's cards, 2 packets of Raeann's cards and 4 packets of Victoria's cards add up to 490 cards. How many cards do they have altogether?
| |
Zara |
Raeann |
Victoria |
| Number of packets |
9 |
4 |
6 |
| Number of cards |
36 u |
36 u |
36 u |
| Number of cards in each packet |
4 u |
9 u |
6 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 9, 4 and 6 = 36
Number of cards that each child has = 36 u
Number of cards in 1 packet of Zara's cards = 36 u ÷ 9 = 4 u
Number of cards in 1 packet of Raeann's cards = 36 u ÷ 4 = 9 u
Number of cards in 1 packet of Victoria's cards = 36 u ÷ 6 = 6 u
Number of cards in 7 packets of Zara's cards, 2 packets of Raeann's cards and 4 packets of Victoria's cards
= (7 x 4 u) + (2 x 9 u) + (4 x 6 u)
= 28 u + 18 u + 24 u
= 70 u
70 u = 490
1 u = 490 ÷ 70 = 7
Total number of cards that they have
= 3 x 36 u
= 108 u
= 108 x 7
= 756
Answer(s): 756
