Zara, Joelle and Emma have equal number of pens. Zara packs all her pens equally into 6 packets. Joelle packs all her pens equally into 8 packets. Emma packs all her pens equally into 4 packets. 4 packets of Zara's pens, 6 packets of Joelle's pens and 2 packets of Emma's pens add up to 322 pens. How many pens do they have altogether?
| |
Zara |
Joelle |
Emma |
| Number of packets |
6 |
8 |
4 |
| Number of pens |
24 u |
24 u |
24 u |
| Number of pens in each packet |
4 u |
3 u |
6 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 6, 8 and 4 = 24
Number of pens that each child has = 24 u
Number of pens in 1 packet of Zara's pens = 24 u ÷ 6 = 4 u
Number of pens in 1 packet of Joelle's pens = 24 u ÷ 8 = 3 u
Number of pens in 1 packet of Emma's pens = 24 u ÷ 4 = 6 u
Number of pens in 4 packets of Zara's pens, 6 packets of Joelle's pens and 2 packets of Emma's pens
= (4 x 4 u) + (6 x 3 u) + (2 x 6 u)
= 16 u + 18 u + 12 u
= 46 u
46 u = 322
1 u = 322 ÷ 46 = 7
Total number of pens that they have
= 3 x 24 u
= 72 u
= 72 x 7
= 504
Answer(s): 504
