Sarah, Kylie and Sabrina have equal number of erasers. Sarah packs all her erasers equally into 5 packets. Kylie packs all her erasers equally into 4 packets. Sabrina packs all her erasers equally into 10 packets. 4 packets of Sarah's erasers, 3 packets of Kylie's erasers and 8 packets of Sabrina's erasers add up to 329 erasers. How many erasers do they have altogether?
| |
Sarah |
Kylie |
Sabrina |
| Number of packets |
5 |
4 |
10 |
| Number of erasers |
20 u |
20 u |
20 u |
| Number of erasers in each packet |
4 u |
5 u |
2 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, 4 and 10 = 20
Number of erasers that each child has = 20 u
Number of erasers in 1 packet of Sarah's erasers = 20 u ÷ 5 = 4 u
Number of erasers in 1 packet of Kylie's erasers = 20 u ÷ 4 = 5 u
Number of erasers in 1 packet of Sabrina's erasers = 20 u ÷ 10 = 2 u
Number of erasers in 4 packets of Sarah's erasers, 3 packets of Kylie's erasers and 8 packets of Sabrina's erasers
= (4 x 4 u) + (3 x 5 u) + (8 x 2 u)
= 16 u + 15 u + 16 u
= 47 u
47 u = 329
1 u = 329 ÷ 47 = 7
Total number of erasers that they have
= 3 x 20 u
= 60 u
= 60 x 7
= 420
Answer(s): 420
