Ivory, Tammy and Jaslyn have equal number of pens. Ivory packs all her pens equally into 6 packets. Tammy packs all her pens equally into 10 packets. Jaslyn packs all her pens equally into 5 packets. 3 packets of Ivory's pens, 2 packets of Tammy's pens and 4 packets of Jaslyn's pens add up to 450 pens. How many pens do they have altogether?

	Ivory	Tammy	Jaslyn
Number of packets	6	10	5
Number of pens	30 u	30 u	30 u
Number of pens in each packet	5 u	3 u	6 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 6, 10 and 5 = 30

Number of pens that each child has = 30 u

Number of pens in 1 packet of Ivory's pens = 30 u ÷ 6 = 5 u
Number of pens in 1 packet of Tammy's pens = 30 u ÷ 10 = 3 u
Number of pens in 1 packet of Jaslyn's pens = 30 u ÷ 5 = 6 u

Number of pens in 3 packets of Ivory's pens, 2 packets of Tammy's pens and 4 packets of Jaslyn's pens
= (3 x 5 u) + (2 x 3 u) + (4 x 6 u)
= 15 u + 6 u + 24 u
= 45 u

45 u = 450

1 u = 450 ÷ 45 = 10

Total number of pens that they have
= 3 x 30 u
= 90 u
= 90 x 10
= 900

Answer(s): 900