Usha, Zara and Anna have equal number of pens. Usha packs all her pens equally into 4 packets. Zara packs all her pens equally into 6 packets. Anna packs all her pens equally into 8 packets. 3 packets of Usha's pens, 2 packets of Zara's pens and 6 packets of Anna's pens add up to 88 pens. How many pens do they have altogether?

	Usha	Zara	Anna
Number of packets	4	6	8
Number of pens	24 u	24 u	24 u
Number of pens in each packet	6 u	4 u	3 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 4, 6 and 8 = 24

Number of pens that each child has = 24 u

Number of pens in 1 packet of Usha's pens = 24 u ÷ 4 = 6 u
Number of pens in 1 packet of Zara's pens = 24 u ÷ 6 = 4 u
Number of pens in 1 packet of Anna's pens = 24 u ÷ 8 = 3 u

Number of pens in 3 packets of Usha's pens, 2 packets of Zara's pens and 6 packets of Anna's pens
= (3 x 6 u) + (2 x 4 u) + (6 x 3 u)
= 18 u + 8 u + 18 u
= 44 u

44 u = 88

1 u = 88 ÷ 44 = 2

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

Answer(s): 144