Barbara, Tiffany and Xylia have equal number of pencils. Barbara packs all her pencils equally into 6 packets. Tiffany packs all her pencils equally into 5 packets. Xylia packs all her pencils equally into 10 packets. 5 packets of Barbara's pencils, 3 packets of Tiffany's pencils and 2 packets of Xylia's pencils add up to 441 pencils. How many pencils do they have altogether?

	Barbara	Tiffany	Xylia
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 Barbara's pencils = 30 u ÷ 6 = 5 u
Number of pencils in 1 packet of Tiffany's pencils = 30 u ÷ 5 = 6 u
Number of pencils in 1 packet of Xylia's pencils = 30 u ÷ 10 = 3 u

Number of pencils in 5 packets of Barbara's pencils, 3 packets of Tiffany's pencils and 2 packets of Xylia's pencils
= (5 x 5 u) + (3 x 6 u) + (2 x 3 u)
= 25 u + 18 u + 6 u
= 49 u

49 u = 441

1 u = 441 ÷ 49 = 9

Total number of pencils that they have
= 3 x 30 u
= 90 u
= 90 x 9
= 810

Answer(s): 810