Lynn, Gem and Jen have equal number of pencils. Lynn packs all her pencils equally into 6 packets. Gem packs all her pencils equally into 5 packets. Jen packs all her pencils equally into 10 packets. 2 packets of Lynn's pencils, 4 packets of Gem's pencils and 6 packets of Jen's pencils add up to 520 pencils. How many pencils do they have altogether?

	Lynn	Gem	Jen
Number of packets	6	5	10
Number of pencils	30 u	30 u	30 u
Number of pencils in each packet	5 u	6 u	3 u

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

All the children have equal numbers of pencils. 
Make the number of pencils that each child has the same. LCM of 6, 5 and 10 = 30

Number of pencils that each child has = 30 u

Number of pencils in 1 packet of Lynn's pencils = 30 u ÷ 6 = 5 u
Number of pencils in 1 packet of Gem's pencils = 30 u ÷ 5 = 6 u
Number of pencils in 1 packet of Jen's pencils = 30 u ÷ 10 = 3 u

Number of pencils in 2 packets of Lynn's pencils, 4 packets of Gem's pencils and 6 packets of Jen's pencils
= (2 x 5 u) + (4 x 6 u) + (6 x 3 u)
= 10 u + 24 u + 18 u
= 52 u

52 u = 520

1 u = 520 ÷ 52 = 10

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

Answer(s): 900