Roshel, Risa and Gwen have equal number of coins. Roshel packs all her coins equally into 10 packets. Risa packs all her coins equally into 4 packets. Gwen packs all her coins equally into 8 packets. 8 packets of Roshel's coins, 2 packets of Risa's coins and 3 packets of Gwen's coins add up to 402 coins. How many coins do they have altogether?
| |
Roshel |
Risa |
Gwen |
| Number of packets |
10 |
4 |
8 |
| Number of coins |
40 u |
40 u |
40 u |
| Number of coins in each packet |
4 u |
10 u |
5 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 10, 4 and 8 = 40
Number of coins that each child has = 40 u
Number of coins in 1 packet of Roshel's coins = 40 u ÷ 10 = 4 u
Number of coins in 1 packet of Risa's coins = 40 u ÷ 4 = 10 u
Number of coins in 1 packet of Gwen's coins = 40 u ÷ 8 = 5 u
Number of coins in 8 packets of Roshel's coins, 2 packets of Risa's coins and 3 packets of Gwen's coins
= (8 x 4 u) + (2 x 10 u) + (3 x 5 u)
= 32 u + 20 u + 15 u
= 67 u
67 u = 402
1 u = 402 ÷ 67 = 6
Total number of coins that they have
= 3 x 40 u
= 120 u
= 120 x 6
= 720
Answer(s): 720
