Ivory, Xuan and Eva have equal number of pencils. Ivory packs all her pencils equally into 5 packets. Xuan packs all her pencils equally into 10 packets. Eva packs all her pencils equally into 6 packets. 2 packets of Ivory's pencils, 8 packets of Xuan's pencils and 4 packets of Eva's pencils add up to 168 pencils. How many pencils do they have altogether?

	Ivory	Xuan	Eva
Number of packets	5	10	6
Number of pencils	30 u	30 u	30 u
Number of pencils in each packet	6 u	3 u	5 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 5, 10 and 6 = 30

Number of pencils that each child has = 30 u

Number of pencils in 1 packet of Ivory's pencils = 30 u ÷ 5 = 6 u
Number of pencils in 1 packet of Xuan's pencils = 30 u ÷ 10 = 3 u
Number of pencils in 1 packet of Eva's pencils = 30 u ÷ 6 = 5 u

Number of pencils in 2 packets of Ivory's pencils, 8 packets of Xuan's pencils and 4 packets of Eva's pencils
= (2 x 6 u) + (8 x 3 u) + (4 x 5 u)
= 12 u + 24 u + 20 u
= 56 u

56 u = 168

1 u = 168 ÷ 56 = 3

Total number of pencils that they have
= 3 x 30 u
= 90 u
= 90 x 3
= 270

Answer(s): 270