Pamela, Irene and Yen have equal number of erasers. Pamela packs all her erasers equally into 3 packets. Irene packs all her erasers equally into 9 packets. Yen packs all her erasers equally into 4 packets. 2 packets of Pamela's erasers, 5 packets of Irene's erasers and 3 packets of Yen's erasers add up to 284 erasers. How many erasers do they have altogether?
| |
Pamela |
Irene |
Yen |
| Number of packets |
3 |
9 |
4 |
| Number of erasers |
36 u |
36 u |
36 u |
| Number of erasers in each packet |
12 u |
4 u |
9 u |
All the erasers can be put into the packets without remainder.
All the children have equal numbers of erasers.
Make the number of erasers that each child has the same. LCM of 3, 9 and 4 = 36
Number of erasers that each child has = 36 u
Number of erasers in 1 packet of Pamela's erasers = 36 u ÷ 3 = 12 u
Number of erasers in 1 packet of Irene's erasers = 36 u ÷ 9 = 4 u
Number of erasers in 1 packet of Yen's erasers = 36 u ÷ 4 = 9 u
Number of erasers in 2 packets of Pamela's erasers, 5 packets of Irene's erasers and 3 packets of Yen's erasers
= (2 x 12 u) + (5 x 4 u) + (3 x 9 u)
= 24 u + 20 u + 27 u
= 71 u
71 u = 284
1 u = 284 ÷ 71 = 4
Total number of erasers that they have
= 3 x 36 u
= 108 u
= 108 x 4
= 432
Answer(s): 432
