Cindy, Victoria and Raeann have equal number of cards. Cindy packs all her cards equally into 6 packets. Victoria packs all her cards equally into 10 packets. Raeann packs all her cards equally into 4 packets. 4 packets of Cindy's cards, 6 packets of Victoria's cards and 2 packets of Raeann's cards add up to 424 cards. How many cards do they have altogether?
| |
Cindy |
Victoria |
Raeann |
| Number of packets |
6 |
10 |
4 |
| Number of cards |
60 u |
60 u |
60 u |
| Number of cards in each packet |
10 u |
6 u |
15 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, 10 and 4 = 60
Number of cards that each child has = 60 u
Number of cards in 1 packet of Cindy's cards = 60 u ÷ 6 = 10 u
Number of cards in 1 packet of Victoria's cards = 60 u ÷ 10 = 6 u
Number of cards in 1 packet of Raeann's cards = 60 u ÷ 4 = 15 u
Number of cards in 4 packets of Cindy's cards, 6 packets of Victoria's cards and 2 packets of Raeann's cards
= (4 x 10 u) + (6 x 6 u) + (2 x 15 u)
= 40 u + 36 u + 30 u
= 106 u
106 u = 424
1 u = 424 ÷ 106 = 4
Total number of cards that they have
= 3 x 60 u
= 180 u
= 180 x 4
= 720
Answer(s): 720
