Xuan, Cathy and Linda have equal number of beads. Xuan packs all her beads equally into 5 packets. Cathy packs all her beads equally into 8 packets. Linda packs all her beads equally into 10 packets. 2 packets of Xuan's beads, 3 packets of Cathy's beads and 7 packets of Linda's beads add up to 295 beads. How many beads do they have altogether?
| |
Xuan |
Cathy |
Linda |
| Number of packets |
5 |
8 |
10 |
| Number of beads |
40 u |
40 u |
40 u |
| Number of beads in each packet |
8 u |
5 u |
4 u |
All the beads can be put into the packets without remainder.
All the children have equal numbers of beads.
Make the number of beads that each child has the same. LCM of 5, 8 and 10 = 40
Number of beads that each child has = 40 u
Number of beads in 1 packet of Xuan's beads = 40 u ÷ 5 = 8 u
Number of beads in 1 packet of Cathy's beads = 40 u ÷ 8 = 5 u
Number of beads in 1 packet of Linda's beads = 40 u ÷ 10 = 4 u
Number of beads in 2 packets of Xuan's beads, 3 packets of Cathy's beads and 7 packets of Linda's beads
= (2 x 8 u) + (3 x 5 u) + (7 x 4 u)
= 16 u + 15 u + 28 u
= 59 u
59 u = 295
1 u = 295 ÷ 59 = 5
Total number of beads that they have
= 3 x 40 u
= 120 u
= 120 x 5
= 600
Answer(s): 600
