Emily, Yen and Shiyun have equal number of beads. Emily packs all her beads equally into 9 packets. Yen packs all her beads equally into 3 packets. Shiyun packs all her beads equally into 4 packets. 6 packets of Emily's beads, 2 packets of Yen's beads and 3 packets of Shiyun's beads add up to 225 beads. How many beads do they have altogether?
| |
Emily |
Yen |
Shiyun |
| Number of packets |
9 |
3 |
4 |
| Number of beads |
36 u |
36 u |
36 u |
| Number of beads in each packet |
4 u |
12 u |
9 u |
All the beads can be put into the packets without remainder.
All the children have equal numbers of beads.
Make the number of beads that each child has the same. LCM of 9, 3 and 4 = 36
Number of beads that each child has = 36 u
Number of beads in 1 packet of Emily's beads = 36 u ÷ 9 = 4 u
Number of beads in 1 packet of Yen's beads = 36 u ÷ 3 = 12 u
Number of beads in 1 packet of Shiyun's beads = 36 u ÷ 4 = 9 u
Number of beads in 6 packets of Emily's beads, 2 packets of Yen's beads and 3 packets of Shiyun's beads
= (6 x 4 u) + (2 x 12 u) + (3 x 9 u)
= 24 u + 24 u + 27 u
= 75 u
75 u = 225
1 u = 225 ÷ 75 = 3
Total number of beads that they have
= 3 x 36 u
= 108 u
= 108 x 3
= 324
Answer(s): 324
