Tina, Xuan and Fanny have equal number of marbles. Tina packs all her marbles equally into 8 packets. Xuan packs all her marbles equally into 5 packets. Fanny packs all her marbles equally into 10 packets. 3 packets of Tina's marbles, 4 packets of Xuan's marbles and 5 packets of Fanny's marbles add up to 469 marbles. How many marbles do they have altogether?
| |
Tina |
Xuan |
Fanny |
| Number of packets |
8 |
5 |
10 |
| Number of marbles |
40 u |
40 u |
40 u |
| Number of marbles in each packet |
5 u |
8 u |
4 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 8, 5 and 10 = 40
Number of marbles that each child has = 40 u
Number of marbles in 1 packet of Tina's marbles = 40 u ÷ 8 = 5 u
Number of marbles in 1 packet of Xuan's marbles = 40 u ÷ 5 = 8 u
Number of marbles in 1 packet of Fanny's marbles = 40 u ÷ 10 = 4 u
Number of marbles in 3 packets of Tina's marbles, 4 packets of Xuan's marbles and 5 packets of Fanny's marbles
= (3 x 5 u) + (4 x 8 u) + (5 x 4 u)
= 15 u + 32 u + 20 u
= 67 u
67 u = 469
1 u = 469 ÷ 67 = 7
Total number of marbles that they have
= 3 x 40 u
= 120 u
= 120 x 7
= 840
Answer(s): 840
