Gwen, Pamela and Lynn have equal number of beads. Gwen packs all her beads equally into 5 packets. Pamela packs all her beads equally into 10 packets. Lynn packs all her beads equally into 8 packets. 4 packets of Gwen's beads, 6 packets of Pamela's beads and 2 packets of Lynn's beads add up to 330 beads. How many beads do they have altogether?
| |
Gwen |
Pamela |
Lynn |
| Number of packets |
5 |
10 |
8 |
| Number of beads |
40 u |
40 u |
40 u |
| Number of beads in each packet |
8 u |
4 u |
5 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, 10 and 8 = 40
Number of beads that each child has = 40 u
Number of beads in 1 packet of Gwen's beads = 40 u ÷ 5 = 8 u
Number of beads in 1 packet of Pamela's beads = 40 u ÷ 10 = 4 u
Number of beads in 1 packet of Lynn's beads = 40 u ÷ 8 = 5 u
Number of beads in 4 packets of Gwen's beads, 6 packets of Pamela's beads and 2 packets of Lynn's beads
= (4 x 8 u) + (6 x 4 u) + (2 x 5 u)
= 32 u + 24 u + 10 u
= 66 u
66 u = 330
1 u = 330 ÷ 66 = 5
Total number of beads that they have
= 3 x 40 u
= 120 u
= 120 x 5
= 600
Answer(s): 600
