Kathy, Rachel and Shannon have equal number of beads. Kathy packs all her beads equally into 3 packets. Rachel packs all her beads equally into 6 packets. Shannon packs all her beads equally into 8 packets. 2 packets of Kathy's beads, 4 packets of Rachel's beads and 6 packets of Shannon's beads add up to 500 beads. How many beads do they have altogether?

	Kathy	Rachel	Shannon
Number of packets	3	6	8
Number of beads	24 u	24 u	24 u
Number of beads in each packet	8 u	4 u	3 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 3, 6 and 8 = 24

Number of beads that each child has = 24 u

Number of beads in 1 packet of Kathy's beads = 24 u ÷ 3 = 8 u
Number of beads in 1 packet of Rachel's beads = 24 u ÷ 6 = 4 u
Number of beads in 1 packet of Shannon's beads = 24 u ÷ 8 = 3 u

Number of beads in 2 packets of Kathy's beads, 4 packets of Rachel's beads and 6 packets of Shannon's beads
= (2 x 8 u) + (4 x 4 u) + (6 x 3 u)
= 16 u + 16 u + 18 u
= 50 u

50 u = 500

1 u = 500 ÷ 50 = 10

Total number of beads that they have
= 3 x 24 u
= 72 u
= 72 x 10
= 720

Answer(s): 720