Dana, Winnie and Xandra have equal number of stickers. Dana packs all her stickers equally into 3 packets. Winnie packs all her stickers equally into 8 packets. Xandra packs all her stickers equally into 6 packets. 2 packets of Dana's stickers, 3 packets of Winnie's stickers and 4 packets of Xandra's stickers add up to 369 stickers. How many stickers do they have altogether?
| |
Dana |
Winnie |
Xandra |
| Number of packets |
3 |
8 |
6 |
| Number of stickers |
24 u |
24 u |
24 u |
| Number of stickers in each packet |
8 u |
3 u |
4 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 3, 8 and 6 = 24
Number of stickers that each child has = 24 u
Number of stickers in 1 packet of Dana's stickers = 24 u ÷ 3 = 8 u
Number of stickers in 1 packet of Winnie's stickers = 24 u ÷ 8 = 3 u
Number of stickers in 1 packet of Xandra's stickers = 24 u ÷ 6 = 4 u
Number of stickers in 2 packets of Dana's stickers, 3 packets of Winnie's stickers and 4 packets of Xandra's stickers
= (2 x 8 u) + (3 x 3 u) + (4 x 4 u)
= 16 u + 9 u + 16 u
= 41 u
41 u = 369
1 u = 369 ÷ 41 = 9
Total number of stickers that they have
= 3 x 24 u
= 72 u
= 72 x 9
= 648
Answer(s): 648
