Esther, Tina and Xuan have equal number of erasers. Esther packs all her erasers equally into 4 packets. Tina packs all her erasers equally into 10 packets. Xuan packs all her erasers equally into 6 packets. 3 packets of Esther's erasers, 7 packets of Tina's erasers and 2 packets of Xuan's erasers add up to 214 erasers. How many erasers do they have altogether?
| |
Esther |
Tina |
Xuan |
| Number of packets |
4 |
10 |
6 |
| Number of erasers |
60 u |
60 u |
60 u |
| Number of erasers in each packet |
15 u |
6 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 4, 10 and 6 = 60
Number of erasers that each child has = 60 u
Number of erasers in 1 packet of Esther's erasers = 60 u ÷ 4 = 15 u
Number of erasers in 1 packet of Tina's erasers = 60 u ÷ 10 = 6 u
Number of erasers in 1 packet of Xuan's erasers = 60 u ÷ 6 = 10 u
Number of erasers in 3 packets of Esther's erasers, 7 packets of Tina's erasers and 2 packets of Xuan's erasers
= (3 x 15 u) + (7 x 6 u) + (2 x 10 u)
= 45 u + 42 u + 20 u
= 107 u
107 u = 214
1 u = 214 ÷ 107 = 2
Total number of erasers that they have
= 3 x 60 u
= 180 u
= 180 x 2
= 360
Answer(s): 360
