Sarah, Jane and Erika have equal number of pens. Sarah packs all her pens equally into 9 packets. Jane packs all her pens equally into 3 packets. Erika packs all her pens equally into 5 packets. 5 packets of Sarah's pens, 2 packets of Jane's pens and 4 packets of Erika's pens add up to 728 pens. How many pens do they have altogether?
| |
Sarah |
Jane |
Erika |
| Number of packets |
9 |
3 |
5 |
| Number of pens |
45 u |
45 u |
45 u |
| Number of pens in each packet |
5 u |
15 u |
9 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 9, 3 and 5 = 45
Number of pens that each child has = 45 u
Number of pens in 1 packet of Sarah's pens = 45 u ÷ 9 = 5 u
Number of pens in 1 packet of Jane's pens = 45 u ÷ 3 = 15 u
Number of pens in 1 packet of Erika's pens = 45 u ÷ 5 = 9 u
Number of pens in 5 packets of Sarah's pens, 2 packets of Jane's pens and 4 packets of Erika's pens
= (5 x 5 u) + (2 x 15 u) + (4 x 9 u)
= 25 u + 30 u + 36 u
= 91 u
91 u = 728
1 u = 728 ÷ 91 = 8
Total number of pens that they have
= 3 x 45 u
= 135 u
= 135 x 8
= 1080
Answer(s): 1080
