Hilda, Marion and Kylie have equal number of beads. Hilda packs all her beads equally into 10 packets. Marion packs all her beads equally into 6 packets. Kylie packs all her beads equally into 5 packets. 2 packets of Hilda's beads, 5 packets of Marion's beads and 3 packets of Kylie's beads add up to 294 beads. How many beads do they have altogether?

	Hilda	Marion	Kylie
Number of packets	10	6	5
Number of beads	30 u	30 u	30 u
Number of beads in each packet	3 u	5 u	6 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 10, 6 and 5 = 30

Number of beads that each child has = 30 u

Number of beads in 1 packet of Hilda's beads = 30 u ÷ 10 = 3 u
Number of beads in 1 packet of Marion's beads = 30 u ÷ 6 = 5 u
Number of beads in 1 packet of Kylie's beads = 30 u ÷ 5 = 6 u

Number of beads in 2 packets of Hilda's beads, 5 packets of Marion's beads and 3 packets of Kylie's beads
= (2 x 3 u) + (5 x 5 u) + (3 x 6 u)
= 6 u + 25 u + 18 u
= 49 u

49 u = 294

1 u = 294 ÷ 49 = 6

Total number of beads that they have
= 3 x 30 u
= 90 u
= 90 x 6
= 540

Answer(s): 540