Natalie, Yoko and Elyse have equal number of pens. Natalie packs all her pens equally into 6 packets. Yoko packs all her pens equally into 4 packets. Elyse packs all her pens equally into 10 packets. 5 packets of Natalie's pens, 3 packets of Yoko's pens and 6 packets of Elyse's pens add up to 655 pens. How many pens do they have altogether?
| |
Natalie |
Yoko |
Elyse |
| Number of packets |
6 |
4 |
10 |
| Number of pens |
60 u |
60 u |
60 u |
| Number of pens in each packet |
10 u |
15 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, 4 and 10 = 60
Number of pens that each child has = 60 u
Number of pens in 1 packet of Natalie's pens = 60 u ÷ 6 = 10 u
Number of pens in 1 packet of Yoko's pens = 60 u ÷ 4 = 15 u
Number of pens in 1 packet of Elyse's pens = 60 u ÷ 10 = 6 u
Number of pens in 5 packets of Natalie's pens, 3 packets of Yoko's pens and 6 packets of Elyse's pens
= (5 x 10 u) + (3 x 15 u) + (6 x 6 u)
= 50 u + 45 u + 36 u
= 131 u
131 u = 655
1 u = 655 ÷ 131 = 5
Total number of pens that they have
= 3 x 60 u
= 180 u
= 180 x 5
= 900
Answer(s): 900
