Nick bought fewer than 14 packets of pencils. Each packet contained 14 pencils. He gave his teachers one packet of pencils each before giving an equal number of pencils to his 15 friends and had 4 pencils left. He had less than 5 teachers.
- How many pencils did each of his friends receive?
- What is the maximum number of teachers he could give a packet each to?
Since Nick gave one packet of pencils each to his teachers, the maximum number of packets that Nick could give to his teachers
= 14 - 1
= 13
Since the number of teachers must be less than 5, the maximum number of teachers
= 5 - 1
= 4
If Nick had 4 teachers, the minimum number of packets that Nick could possibly give to his friends
= 13 - 4
= 9
Find out how many packets of pencils can be distributed to his 15 friends to have 4 pencils left.
Number of packets
for friends |
Total number
of pencils |
Number of pencils to
each of his 15 friends |
|
9
|
9 x 14 =
126 |
126 ÷ 15 =
8 r 6 |
x |
10
|
10 x 14 =
140 |
140 ÷ 15 =
9 r 5 |
x |
11
|
11 x 14 =
154 |
154 ÷ 15 =
10 r 4 |
✔ |
(a)
Number of pencils that each of his 15 friends received = 10
(b)
Number of packets that Nick could give to his 15 friends = 11
Maximum number of teachers that Nick could give one packet each to
= 13 - 11
= 2
Answer(s): (a) 10 ; (b) 2
