Jack bought fewer than 12 packets of markers. Each packet contained 14 markers. He gave his teachers one packet of markers each before giving an equal number of markers to his 15 schoolmates and had 8 markers left. He had less than 7 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 Jack gave one packet of markers each to his teachers, the maximum number of packets that Jack could give to his teachers
= 12 - 1
= 11
Since the number of teachers must be less than 7, the maximum number of teachers
= 7 - 1
= 6
If Jack had 6 teachers, the minimum number of packets that Jack could possibly give to his schoolmates
= 11 - 6
= 5
Find out how many packets of markers can be distributed to his 15 schoolmates to have 8 markers left.
Number of packets
for schoolmates |
Total number
of markers |
Number of markers to
each of his 15 schoolmates |
|
5
|
5 x 14 =
70 |
70 ÷ 15 =
4 r 10 |
x |
6
|
6 x 14 =
84 |
84 ÷ 15 =
5 r 9 |
x |
7
|
7 x 14 =
98 |
98 ÷ 15 =
6 r 8 |
✔ |
(a)
Number of markers that each of his 15 schoolmates received = 6
(b)
Number of packets that Jack could give to his 15 schoolmates = 7
Maximum number of teachers that Jack could give one packet each to
= 11 - 7
= 4
Answer(s): (a) 6 ; (b) 4
