Eva, Lucy and Sabrina have equal number of erasers. Eva packs all her erasers equally into 9 packets. Lucy packs all her erasers equally into 6 packets. Sabrina packs all her erasers equally into 3 packets. 4 packets of Eva's erasers, 3 packets of Lucy's erasers and 2 packets of Sabrina's erasers add up to 290 erasers. How many erasers do they have altogether?
| |
Eva |
Lucy |
Sabrina |
| Number of packets |
9 |
6 |
3 |
| Number of erasers |
18 u |
18 u |
18 u |
| Number of erasers in each packet |
2 u |
3 u |
6 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 9, 6 and 3 = 18
Number of erasers that each child has = 18 u
Number of erasers in 1 packet of Eva's erasers = 18 u ÷ 9 = 2 u
Number of erasers in 1 packet of Lucy's erasers = 18 u ÷ 6 = 3 u
Number of erasers in 1 packet of Sabrina's erasers = 18 u ÷ 3 = 6 u
Number of erasers in 4 packets of Eva's erasers, 3 packets of Lucy's erasers and 2 packets of Sabrina's erasers
= (4 x 2 u) + (3 x 3 u) + (2 x 6 u)
= 8 u + 9 u + 12 u
= 29 u
29 u = 290
1 u = 290 ÷ 29 = 10
Total number of erasers that they have
= 3 x 18 u
= 54 u
= 54 x 10
= 540
Answer(s): 540
