Pamela, Raeann and Penelope have equal number of pens. Pamela packs all her pens equally into 4 packets. Raeann packs all her pens equally into 6 packets. Penelope packs all her pens equally into 9 packets. 2 packets of Pamela's pens, 5 packets of Raeann's pens and 7 packets of Penelope's pens add up to 760 pens. How many pens do they have altogether?
| |
Pamela |
Raeann |
Penelope |
| Number of packets |
4 |
6 |
9 |
| Number of pens |
36 u |
36 u |
36 u |
| Number of pens in each packet |
9 u |
6 u |
4 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 4, 6 and 9 = 36
Number of pens that each child has = 36 u
Number of pens in 1 packet of Pamela's pens = 36 u ÷ 4 = 9 u
Number of pens in 1 packet of Raeann's pens = 36 u ÷ 6 = 6 u
Number of pens in 1 packet of Penelope's pens = 36 u ÷ 9 = 4 u
Number of pens in 2 packets of Pamela's pens, 5 packets of Raeann's pens and 7 packets of Penelope's pens
= (2 x 9 u) + (5 x 6 u) + (7 x 4 u)
= 18 u + 30 u + 28 u
= 76 u
76 u = 760
1 u = 760 ÷ 76 = 10
Total number of pens that they have
= 3 x 36 u
= 108 u
= 108 x 10
= 1080
Answer(s): 1080
