Sam bought fewer than 15 packets of pencils. Each packet contained 20 pencils. He gave his teachers one packet of pencils each before giving an equal number of pencils to his 14 classmates and had 2 pencils left. He had less than 4 teachers.
- How many pencils did each of his classmates receive?
- What is the maximum number of teachers he could give a packet each to?
Since Sam gave one packet of pencils each to his teachers, the maximum number of packets that Sam could give to his teachers
= 15 - 1
= 14
Since the number of teachers must be less than 4, the maximum number of teachers
= 4 - 1
= 3
If Sam had 3 teachers, the minimum number of packets that Sam could possibly give to his classmates
= 14 - 3
= 11
Find out how many packets of pencils can be distributed to his 14 classmates to have 8 pencils left.
Number of packets
for classmates |
Total number
of pencils |
Number of pencils to
each of his 14 classmates |
|
11
|
11 x 20 =
220 |
220 ÷ 14 =
15 r 10 |
x |
12
|
12 x 20 =
240 |
240 ÷ 14 =
17 r 2 |
✔ |
(a)
Number of pencils that each of his 14 classmates received = 17
(b)
Number of packets that Sam could give to his 14 classmates = 12
Maximum number of teachers that Sam could give one packet each to
= 14 - 12
= 2
Answer(s): (a) 18 ; (b) 2
