Abi, Jaslyn and Jade have equal number of coins. Abi packs all her coins equally into 3 packets. Jaslyn packs all her coins equally into 5 packets. Jade packs all her coins equally into 10 packets. 2 packets of Abi's coins, 4 packets of Jaslyn's coins and 5 packets of Jade's coins add up to 590 coins. How many coins do they have altogether?
| |
Abi |
Jaslyn |
Jade |
| Number of packets |
3 |
5 |
10 |
| Number of coins |
30 u |
30 u |
30 u |
| Number of coins in each packet |
10 u |
6 u |
3 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 3, 5 and 10 = 30
Number of coins that each child has = 30 u
Number of coins in 1 packet of Abi's coins = 30 u ÷ 3 = 10 u
Number of coins in 1 packet of Jaslyn's coins = 30 u ÷ 5 = 6 u
Number of coins in 1 packet of Jade's coins = 30 u ÷ 10 = 3 u
Number of coins in 2 packets of Abi's coins, 4 packets of Jaslyn's coins and 5 packets of Jade's coins
= (2 x 10 u) + (4 x 6 u) + (5 x 3 u)
= 20 u + 24 u + 15 u
= 59 u
59 u = 590
1 u = 590 ÷ 59 = 10
Total number of coins that they have
= 3 x 30 u
= 90 u
= 90 x 10
= 900
Answer(s): 900
