Oscar bought fewer than 16 packets of pencils. Each packet contained 12 pencils. He gave his teachers one packet of pencils each before giving an equal number of pencils to his 14 schoolmates and had 12 pencils left. He had less than 9 teachers.
- How many pencils did each of his schoolmates receive?
- What is the maximum number of teachers he could give a packet each to?
Since Oscar gave one packet of pencils each to his teachers, the maximum number of packets that Oscar could give to his teachers
= 16 - 1
= 15
Since the number of teachers must be less than 9, the maximum number of teachers
= 9 - 1
= 8
If Oscar had 8 teachers, the minimum number of packets that Oscar could possibly give to his schoolmates
= 15 - 8
= 7
Find out how many packets of pencils can be distributed to his 14 schoolmates to have 10 pencils left.
Number of packets
for schoolmates |
Total number
of pencils |
Number of pencils to
each of his 14 schoolmates |
|
7
|
7 x 12 =
84 |
84 ÷ 14 =
6 r 0 |
x |
8
|
8 x 12 =
96 |
96 ÷ 14 =
6 r 12 |
✔ |
(a)
Number of pencils that each of his 14 schoolmates received = 6
(b)
Number of packets that Oscar could give to his 14 schoolmates = 8
Maximum number of teachers that Oscar could give one packet each to
= 15 - 8
= 7
Answer(s): (a) 7 ; (b) 7
