Risa, Pamela and Joelle have equal number of pencils. Risa packs all her pencils equally into 10 packets. Pamela packs all her pencils equally into 6 packets. Joelle packs all her pencils equally into 3 packets. 4 packets of Risa's pencils, 5 packets of Pamela's pencils and 2 packets of Joelle's pencils add up to 114 pencils. How many pencils do they have altogether?

	Risa	Pamela	Joelle
Number of packets	10	6	3
Number of pencils	30 u	30 u	30 u
Number of pencils in each packet	3 u	5 u	10 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 10, 6 and 3 = 30

Number of pencils that each child has = 30 u

Number of pencils in 1 packet of Risa's pencils = 30 u ÷ 10 = 3 u
Number of pencils in 1 packet of Pamela's pencils = 30 u ÷ 6 = 5 u
Number of pencils in 1 packet of Joelle's pencils = 30 u ÷ 3 = 10 u

Number of pencils in 4 packets of Risa's pencils, 5 packets of Pamela's pencils and 2 packets of Joelle's pencils
= (4 x 3 u) + (5 x 5 u) + (2 x 10 u)
= 12 u + 25 u + 20 u
= 57 u

57 u = 114

1 u = 114 ÷ 57 = 2

Total number of pencils that they have
= 3 x 30 u
= 90 u
= 90 x 2
= 180

Answer(s): 180