Sabrina, Xandra and Marion have equal number of marbles. Sabrina packs all her marbles equally into 9 packets. Xandra packs all her marbles equally into 6 packets. Marion packs all her marbles equally into 3 packets. 6 packets of Sabrina's marbles, 3 packets of Xandra's marbles and 2 packets of Marion's marbles add up to 165 marbles. How many marbles do they have altogether?
| |
Sabrina |
Xandra |
Marion |
| Number of packets |
9 |
6 |
3 |
| Number of marbles |
18 u |
18 u |
18 u |
| Number of marbles in each packet |
2 u |
3 u |
6 u |
All the marbles can be put into the packets without remainder.
All the children have equal numbers of marbles.
Make the number of marbles that each child has the same. LCM of 9, 6 and 3 = 18
Number of marbles that each child has = 18 u
Number of marbles in 1 packet of Sabrina's marbles = 18 u ÷ 9 = 2 u
Number of marbles in 1 packet of Xandra's marbles = 18 u ÷ 6 = 3 u
Number of marbles in 1 packet of Marion's marbles = 18 u ÷ 3 = 6 u
Number of marbles in 6 packets of Sabrina's marbles, 3 packets of Xandra's marbles and 2 packets of Marion's marbles
= (6 x 2 u) + (3 x 3 u) + (2 x 6 u)
= 12 u + 9 u + 12 u
= 33 u
33 u = 165
1 u = 165 ÷ 33 = 5
Total number of marbles that they have
= 3 x 18 u
= 54 u
= 54 x 5
= 270
Answer(s): 270
