Olivia, Jane and Opal have equal number of marbles. Olivia packs all her marbles equally into 6 packets. Jane packs all her marbles equally into 10 packets. Opal packs all her marbles equally into 5 packets. 4 packets of Olivia's marbles, 2 packets of Jane's marbles and 3 packets of Opal's marbles add up to 88 marbles. How many marbles do they have altogether?
| |
Olivia |
Jane |
Opal |
| Number of packets |
6 |
10 |
5 |
| Number of marbles |
30 u |
30 u |
30 u |
| Number of marbles in each packet |
5 u |
3 u |
6 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 6, 10 and 5 = 30
Number of marbles that each child has = 30 u
Number of marbles in 1 packet of Olivia's marbles = 30 u ÷ 6 = 5 u
Number of marbles in 1 packet of Jane's marbles = 30 u ÷ 10 = 3 u
Number of marbles in 1 packet of Opal's marbles = 30 u ÷ 5 = 6 u
Number of marbles in 4 packets of Olivia's marbles, 2 packets of Jane's marbles and 3 packets of Opal's marbles
= (4 x 5 u) + (2 x 3 u) + (3 x 6 u)
= 20 u + 6 u + 18 u
= 44 u
44 u = 88
1 u = 88 ÷ 44 = 2
Total number of marbles that they have
= 3 x 30 u
= 90 u
= 90 x 2
= 180
Answer(s): 180
