Gillian, Xylia and Tammy have equal number of marbles. Gillian packs all her marbles equally into 10 packets. Xylia packs all her marbles equally into 4 packets. Tammy packs all her marbles equally into 8 packets. 8 packets of Gillian's marbles, 2 packets of Xylia's marbles and 3 packets of Tammy's marbles add up to 134 marbles. How many marbles do they have altogether?
| |
Gillian |
Xylia |
Tammy |
| Number of packets |
10 |
4 |
8 |
| Number of marbles |
40 u |
40 u |
40 u |
| Number of marbles in each packet |
4 u |
10 u |
5 u |
All the marbles can be put into the packets without remainder.
All the children have equal numbers of marbles.
Make the number of marbles that each child has the same. LCM of 10, 4 and 8 = 40
Number of marbles that each child has = 40 u
Number of marbles in 1 packet of Gillian's marbles = 40 u ÷ 10 = 4 u
Number of marbles in 1 packet of Xylia's marbles = 40 u ÷ 4 = 10 u
Number of marbles in 1 packet of Tammy's marbles = 40 u ÷ 8 = 5 u
Number of marbles in 8 packets of Gillian's marbles, 2 packets of Xylia's marbles and 3 packets of Tammy's marbles
= (8 x 4 u) + (2 x 10 u) + (3 x 5 u)
= 32 u + 20 u + 15 u
= 67 u
67 u = 134
1 u = 134 ÷ 67 = 2
Total number of marbles that they have
= 3 x 40 u
= 120 u
= 120 x 2
= 240
Answer(s): 240
