Esther, Pamela and Jaslyn have equal number of marbles. Esther packs all her marbles equally into 6 packets. Pamela packs all her marbles equally into 4 packets. Jaslyn packs all her marbles equally into 8 packets. 4 packets of Esther's marbles, 3 packets of Pamela's marbles and 7 packets of Jaslyn's marbles add up to 385 marbles. How many marbles do they have altogether?

	Esther	Pamela	Jaslyn
Number of packets	6	4	8
Number of marbles	24 u	24 u	24 u
Number of marbles in each packet	4 u	6 u	3 u

All the marbles can be put into the packets without remainder.

All the children have equal numbers of marbles. 
Make the number of marbles that each child has the same. LCM of 6, 4 and 8 = 24

Number of marbles that each child has = 24 u

Number of marbles in 1 packet of Esther's marbles = 24 u ÷ 6 = 4 u
Number of marbles in 1 packet of Pamela's marbles = 24 u ÷ 4 = 6 u
Number of marbles in 1 packet of Jaslyn's marbles = 24 u ÷ 8 = 3 u

Number of marbles in 4 packets of Esther's marbles, 3 packets of Pamela's marbles and 7 packets of Jaslyn's marbles
= (4 x 4 u) + (3 x 6 u) + (7 x 3 u)
= 16 u + 18 u + 21 u
= 55 u

55 u = 385

1 u = 385 ÷ 55 = 7

Total number of marbles that they have
= 3 x 24 u
= 72 u
= 72 x 7
= 504

Answer(s): 504