Jane, Risa and Opal have equal number of pencils. Jane packs all her pencils equally into 5 packets. Risa packs all her pencils equally into 4 packets. Opal packs all her pencils equally into 10 packets. 4 packets of Jane's pencils, 3 packets of Risa's pencils and 6 packets of Opal's pencils add up to 86 pencils. How many pencils do they have altogether?

	Jane	Risa	Opal
Number of packets	5	4	10
Number of pencils	20 u	20 u	20 u
Number of pencils in each packet	4 u	5 u	2 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, 4 and 10 = 20

Number of pencils that each child has = 20 u

Number of pencils in 1 packet of Jane's pencils = 20 u ÷ 5 = 4 u
Number of pencils in 1 packet of Risa's pencils = 20 u ÷ 4 = 5 u
Number of pencils in 1 packet of Opal's pencils = 20 u ÷ 10 = 2 u

Number of pencils in 4 packets of Jane's pencils, 3 packets of Risa's pencils and 6 packets of Opal's pencils
= (4 x 4 u) + (3 x 5 u) + (6 x 2 u)
= 16 u + 15 u + 12 u
= 43 u

43 u = 86

1 u = 86 ÷ 43 = 2

Total number of pencils that they have
= 3 x 20 u
= 60 u
= 60 x 2
= 120

Answer(s): 120