Ivory, Xandra and Gillian have equal number of stickers. Ivory packs all her stickers equally into 9 packets. Xandra packs all her stickers equally into 6 packets. Gillian packs all her stickers equally into 3 packets. 7 packets of Ivory's stickers, 5 packets of Xandra's stickers and 2 packets of Gillian's stickers add up to 410 stickers. How many stickers do they have altogether?
| |
Ivory |
Xandra |
Gillian |
| Number of packets |
9 |
6 |
3 |
| Number of stickers |
18 u |
18 u |
18 u |
| Number of stickers in each packet |
2 u |
3 u |
6 u |
All the stickers can be put into the packets without remainder.
All the children have equal numbers of stickers.
Make the number of stickers that each child has the same. LCM of 9, 6 and 3 = 18
Number of stickers that each child has = 18 u
Number of stickers in 1 packet of Ivory's stickers = 18 u ÷ 9 = 2 u
Number of stickers in 1 packet of Xandra's stickers = 18 u ÷ 6 = 3 u
Number of stickers in 1 packet of Gillian's stickers = 18 u ÷ 3 = 6 u
Number of stickers in 7 packets of Ivory's stickers, 5 packets of Xandra's stickers and 2 packets of Gillian's stickers
= (7 x 2 u) + (5 x 3 u) + (2 x 6 u)
= 14 u + 15 u + 12 u
= 41 u
41 u = 410
1 u = 410 ÷ 41 = 10
Total number of stickers that they have
= 3 x 18 u
= 54 u
= 54 x 10
= 540
Answer(s): 540
