Usha, Emily and Kathy have equal number of coins. Usha packs all her coins equally into 6 packets. Emily packs all her coins equally into 4 packets. Kathy packs all her coins equally into 9 packets. 4 packets of Usha's coins, 2 packets of Emily's coins and 6 packets of Kathy's coins add up to 132 coins. How many coins do they have altogether?
| |
Usha |
Emily |
Kathy |
| Number of packets |
6 |
4 |
9 |
| Number of coins |
36 u |
36 u |
36 u |
| Number of coins in each packet |
6 u |
9 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 6, 4 and 9 = 36
Number of coins that each child has = 36 u
Number of coins in 1 packet of Usha's coins = 36 u ÷ 6 = 6 u
Number of coins in 1 packet of Emily's coins = 36 u ÷ 4 = 9 u
Number of coins in 1 packet of Kathy's coins = 36 u ÷ 9 = 4 u
Number of coins in 4 packets of Usha's coins, 2 packets of Emily's coins and 6 packets of Kathy's coins
= (4 x 6 u) + (2 x 9 u) + (6 x 4 u)
= 24 u + 18 u + 24 u
= 66 u
66 u = 132
1 u = 132 ÷ 66 = 2
Total number of coins that they have
= 3 x 36 u
= 108 u
= 108 x 2
= 216
Answer(s): 216
