Dana, Hazel and Barbara have equal number of pens. Dana packs all her pens equally into 8 packets. Hazel packs all her pens equally into 6 packets. Barbara packs all her pens equally into 3 packets. 3 packets of Dana's pens, 4 packets of Hazel's pens and 2 packets of Barbara's pens add up to 82 pens. How many pens do they have altogether?

	Dana	Hazel	Barbara
Number of packets	8	6	3
Number of pens	24 u	24 u	24 u
Number of pens in each packet	3 u	4 u	8 u

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

All the children have equal numbers of pens. 
Make the number of pens that each child has the same. LCM of 8, 6 and 3 = 24

Number of pens that each child has = 24 u

Number of pens in 1 packet of Dana's pens = 24 u ÷ 8 = 3 u
Number of pens in 1 packet of Hazel's pens = 24 u ÷ 6 = 4 u
Number of pens in 1 packet of Barbara's pens = 24 u ÷ 3 = 8 u

Number of pens in 3 packets of Dana's pens, 4 packets of Hazel's pens and 2 packets of Barbara's pens
= (3 x 3 u) + (4 x 4 u) + (2 x 8 u)
= 9 u + 16 u + 16 u
= 41 u

41 u = 82

1 u = 82 ÷ 41 = 2

Total number of pens that they have
= 3 x 24 u
= 72 u
= 72 x 2
= 144

Answer(s): 144