Elyse, Vanessa and Betty have equal number of pencils. Elyse packs all her pencils equally into 8 packets. Vanessa packs all her pencils equally into 10 packets. Betty packs all her pencils equally into 5 packets. 3 packets of Elyse's pencils, 6 packets of Vanessa's pencils and 4 packets of Betty's pencils add up to 284 pencils. How many pencils do they have altogether?

	Elyse	Vanessa	Betty
Number of packets	8	10	5
Number of pencils	40 u	40 u	40 u
Number of pencils in each packet	5 u	4 u	8 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 8, 10 and 5 = 40

Number of pencils that each child has = 40 u

Number of pencils in 1 packet of Elyse's pencils = 40 u ÷ 8 = 5 u
Number of pencils in 1 packet of Vanessa's pencils = 40 u ÷ 10 = 4 u
Number of pencils in 1 packet of Betty's pencils = 40 u ÷ 5 = 8 u

Number of pencils in 3 packets of Elyse's pencils, 6 packets of Vanessa's pencils and 4 packets of Betty's pencils
= (3 x 5 u) + (6 x 4 u) + (4 x 8 u)
= 15 u + 24 u + 32 u
= 71 u

71 u = 284

1 u = 284 ÷ 71 = 4

Total number of pencils that they have
= 3 x 40 u
= 120 u
= 120 x 4
= 480

Answer(s): 480