Mark bought fewer than 10 packets of markers. Each packet contained 20 markers. He gave his teachers one packet of markers each before giving an equal number of markers to his 12 schoolmates and had 4 markers left. He had less than 6 teachers.
- How many markers did each of his schoolmates receive?
- What is the maximum number of teachers he could give a packet each to?
Since Mark gave one packet of markers each to his teachers, the maximum number of packets that Mark could give to his teachers
= 10 - 1
= 9
Since the number of teachers must be less than 6, the maximum number of teachers
= 6 - 1
= 5
If Mark had 5 teachers, the minimum number of packets that Mark could possibly give to his schoolmates
= 9 - 5
= 4
Find out how many packets of markers can be distributed to his 12 schoolmates to have 0 markers left.
Number of packets
for schoolmates |
Total number
of markers |
Number of markers to
each of his 12 schoolmates |
|
4
|
4 x 20 =
80 |
80 ÷ 12 =
6 r 8 |
x |
5
|
5 x 20 =
100 |
100 ÷ 12 =
8 r 4 |
✔ |
(a)
Number of markers that each of his 12 schoolmates received = 8
(b)
Number of packets that Mark could give to his 12 schoolmates = 5
Maximum number of teachers that Mark could give one packet each to
= 9 - 5
= 4
Answer(s): (a) 10 ; (b) 4
