Olivia, Barbara and Nicole have equal number of pens. Olivia packs all her pens equally into 10 packets. Barbara packs all her pens equally into 4 packets. Nicole packs all her pens equally into 6 packets. 6 packets of Olivia's pens, 2 packets of Barbara's pens and 5 packets of Nicole's pens add up to 696 pens. How many pens do they have altogether?
| |
Olivia |
Barbara |
Nicole |
| Number of packets |
10 |
4 |
6 |
| Number of pens |
60 u |
60 u |
60 u |
| Number of pens in each packet |
6 u |
15 u |
10 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 10, 4 and 6 = 60
Number of pens that each child has = 60 u
Number of pens in 1 packet of Olivia's pens = 60 u ÷ 10 = 6 u
Number of pens in 1 packet of Barbara's pens = 60 u ÷ 4 = 15 u
Number of pens in 1 packet of Nicole's pens = 60 u ÷ 6 = 10 u
Number of pens in 6 packets of Olivia's pens, 2 packets of Barbara's pens and 5 packets of Nicole's pens
= (6 x 6 u) + (2 x 15 u) + (5 x 10 u)
= 36 u + 30 u + 50 u
= 116 u
116 u = 696
1 u = 696 ÷ 116 = 6
Total number of pens that they have
= 3 x 60 u
= 180 u
= 180 x 6
= 1080
Answer(s): 1080
