Paul bought fewer than 12 packets of pens. Each packet contained 18 pens. He gave his teachers one packet of pens each before giving an equal number of pens to his 14 friends and had 4 pens left. He had less than 6 teachers.
- How many pens did each of his friends receive?
- What is the maximum number of teachers he could give a packet each to?
Since Paul gave one packet of pens each to his teachers, the maximum number of packets that Paul could give to his teachers
= 12 - 1
= 11
Since the number of teachers must be less than 6, the maximum number of teachers
= 6 - 1
= 5
If Paul had 5 teachers, the minimum number of packets that Paul could possibly give to his friends
= 11 - 5
= 6
Find out how many packets of pens can be distributed to his 14 friends to have 4 pens left.
Number of packets
for friends |
Total number
of pens |
Number of pens to
each of his 14 friends |
|
6
|
6 x 18 =
108 |
108 ÷ 14 =
7 r 10 |
x |
7
|
7 x 18 =
126 |
126 ÷ 14 =
9 r 0 |
x |
8
|
8 x 18 =
144 |
144 ÷ 14 =
10 r 4 |
✔ |
(a)
Number of pens that each of his 14 friends received = 10
(b)
Number of packets that Paul could give to his 14 friends = 8
Maximum number of teachers that Paul could give one packet each to
= 11 - 8
= 3
Answer(s): (a) 10 ; (b) 3
