Nicole, Betty and Ivory have equal number of pens. Nicole packs all her pens equally into 7 packets. Betty packs all her pens equally into 8 packets. Ivory packs all her pens equally into 4 packets. 5 packets of Nicole's pens, 4 packets of Betty's pens and 3 packets of Ivory's pens add up to 990 pens. How many pens do they have altogether?

	Nicole	Betty	Ivory
Number of packets	7	8	4
Number of pens	56 u	56 u	56 u
Number of pens in each packet	8 u	7 u	14 u

All the pens can be put into the packets without remainder.

All the children have equal numbers of pens. 
Make the number of pens that each child has the same. LCM of 7, 8 and 4 = 56

Number of pens that each child has = 56 u

Number of pens in 1 packet of Nicole's pens = 56 u ÷ 7 = 8 u
Number of pens in 1 packet of Betty's pens = 56 u ÷ 8 = 7 u
Number of pens in 1 packet of Ivory's pens = 56 u ÷ 4 = 14 u

Number of pens in 5 packets of Nicole's pens, 4 packets of Betty's pens and 3 packets of Ivory's pens
= (5 x 8 u) + (4 x 7 u) + (3 x 14 u)
= 40 u + 28 u + 42 u
= 110 u

110 u = 990

1 u = 990 ÷ 110 = 9

Total number of pens that they have
= 3 x 56 u
= 168 u
= 168 x 9
= 1512

Answer(s): 1512