Tammy, Risa and Lucy have equal number of erasers. Tammy packs all her erasers equally into 10 packets. Risa packs all her erasers equally into 8 packets. Lucy packs all her erasers equally into 4 packets. 5 packets of Tammy's erasers, 7 packets of Risa's erasers and 2 packets of Lucy's erasers add up to 450 erasers. How many erasers do they have altogether?
| |
Tammy |
Risa |
Lucy |
| Number of packets |
10 |
8 |
4 |
| Number of erasers |
40 u |
40 u |
40 u |
| Number of erasers in each packet |
4 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 10, 8 and 4 = 40
Number of erasers that each child has = 40 u
Number of erasers in 1 packet of Tammy's erasers = 40 u ÷ 10 = 4 u
Number of erasers in 1 packet of Risa's erasers = 40 u ÷ 8 = 5 u
Number of erasers in 1 packet of Lucy's erasers = 40 u ÷ 4 = 10 u
Number of erasers in 5 packets of Tammy's erasers, 7 packets of Risa's erasers and 2 packets of Lucy's erasers
= (5 x 4 u) + (7 x 5 u) + (2 x 10 u)
= 20 u + 35 u + 20 u
= 75 u
75 u = 450
1 u = 450 ÷ 75 = 6
Total number of erasers that they have
= 3 x 40 u
= 120 u
= 120 x 6
= 720
Answer(s): 720
