Olivia, Nora and Yen have equal number of coins. Olivia packs all her coins equally into 4 packets. Nora packs all her coins equally into 6 packets. Yen packs all her coins equally into 9 packets. 2 packets of Olivia's coins, 4 packets of Nora's coins and 3 packets of Yen's coins add up to 162 coins. How many coins do they have altogether?
| |
Olivia |
Nora |
Yen |
| Number of packets |
4 |
6 |
9 |
| Number of coins |
36 u |
36 u |
36 u |
| Number of coins in each packet |
9 u |
6 u |
4 u |
All the coins can be put into the packets without remainder.
All the children have equal numbers of coins.
Make the number of coins that each child has the same. LCM of 4, 6 and 9 = 36
Number of coins that each child has = 36 u
Number of coins in 1 packet of Olivia's coins = 36 u ÷ 4 = 9 u
Number of coins in 1 packet of Nora's coins = 36 u ÷ 6 = 6 u
Number of coins in 1 packet of Yen's coins = 36 u ÷ 9 = 4 u
Number of coins in 2 packets of Olivia's coins, 4 packets of Nora's coins and 3 packets of Yen's coins
= (2 x 9 u) + (4 x 6 u) + (3 x 4 u)
= 18 u + 24 u + 12 u
= 54 u
54 u = 162
1 u = 162 ÷ 54 = 3
Total number of coins that they have
= 3 x 36 u
= 108 u
= 108 x 3
= 324
Answer(s): 324
