Jaslyn, Olivia and Emma have equal number of erasers. Jaslyn packs all her erasers equally into 6 packets. Olivia packs all her erasers equally into 5 packets. Emma packs all her erasers equally into 10 packets. 2 packets of Jaslyn's erasers, 4 packets of Olivia's erasers and 3 packets of Emma's erasers add up to 344 erasers. How many erasers do they have altogether?
| |
Jaslyn |
Olivia |
Emma |
| Number of packets |
6 |
5 |
10 |
| Number of erasers |
30 u |
30 u |
30 u |
| Number of erasers in each packet |
5 u |
6 u |
3 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 6, 5 and 10 = 30
Number of erasers that each child has = 30 u
Number of erasers in 1 packet of Jaslyn's erasers = 30 u ÷ 6 = 5 u
Number of erasers in 1 packet of Olivia's erasers = 30 u ÷ 5 = 6 u
Number of erasers in 1 packet of Emma's erasers = 30 u ÷ 10 = 3 u
Number of erasers in 2 packets of Jaslyn's erasers, 4 packets of Olivia's erasers and 3 packets of Emma's erasers
= (2 x 5 u) + (4 x 6 u) + (3 x 3 u)
= 10 u + 24 u + 9 u
= 43 u
43 u = 344
1 u = 344 ÷ 43 = 8
Total number of erasers that they have
= 3 x 30 u
= 90 u
= 90 x 8
= 720
Answer(s): 720
