Barbara, Betty and Jean have equal number of pens. Barbara packs all her pens equally into 10 packets. Betty packs all her pens equally into 6 packets. Jean packs all her pens equally into 3 packets. 6 packets of Barbara's pens, 4 packets of Betty's pens and 2 packets of Jean's pens add up to 522 pens. How many pens do they have altogether?
| |
Barbara |
Betty |
Jean |
| Number of packets |
10 |
6 |
3 |
| Number of pens |
30 u |
30 u |
30 u |
| Number of pens in each packet |
3 u |
5 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, 6 and 3 = 30
Number of pens that each child has = 30 u
Number of pens in 1 packet of Barbara's pens = 30 u ÷ 10 = 3 u
Number of pens in 1 packet of Betty's pens = 30 u ÷ 6 = 5 u
Number of pens in 1 packet of Jean's pens = 30 u ÷ 3 = 10 u
Number of pens in 6 packets of Barbara's pens, 4 packets of Betty's pens and 2 packets of Jean's pens
= (6 x 3 u) + (4 x 5 u) + (2 x 10 u)
= 18 u + 20 u + 20 u
= 58 u
58 u = 522
1 u = 522 ÷ 58 = 9
Total number of pens that they have
= 3 x 30 u
= 90 u
= 90 x 9
= 810
Answer(s): 810
