Gillian, Marion and Gabby have equal number of erasers. Gillian packs all her erasers equally into 5 packets. Marion packs all her erasers equally into 8 packets. Gabby packs all her erasers equally into 4 packets. 4 packets of Gillian's erasers, 5 packets of Marion's erasers and 3 packets of Gabby's erasers add up to 261 erasers. How many erasers do they have altogether?
| |
Gillian |
Marion |
Gabby |
| Number of packets |
5 |
8 |
4 |
| Number of erasers |
40 u |
40 u |
40 u |
| Number of erasers in each packet |
8 u |
5 u |
10 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 5, 8 and 4 = 40
Number of erasers that each child has = 40 u
Number of erasers in 1 packet of Gillian's erasers = 40 u ÷ 5 = 8 u
Number of erasers in 1 packet of Marion's erasers = 40 u ÷ 8 = 5 u
Number of erasers in 1 packet of Gabby's erasers = 40 u ÷ 4 = 10 u
Number of erasers in 4 packets of Gillian's erasers, 5 packets of Marion's erasers and 3 packets of Gabby's erasers
= (4 x 8 u) + (5 x 5 u) + (3 x 10 u)
= 32 u + 25 u + 30 u
= 87 u
87 u = 261
1 u = 261 ÷ 87 = 3
Total number of erasers that they have
= 3 x 40 u
= 120 u
= 120 x 3
= 360
Answer(s): 360
