Jeremy bought fewer than 15 packets of notebooks. Each packet contained 14 notebooks. He gave his teachers one packet of notebooks each before giving an equal number of notebooks to his 15 classmates and had 5 notebooks left. He had less than 8 teachers.
- How many notebooks did each of his classmates receive?
- What is the maximum number of teachers he could give a packet each to?
Since Jeremy gave one packet of notebooks each to his teachers, the maximum number of packets that Jeremy could give to his teachers
= 15 - 1
= 14
Since the number of teachers must be less than 8, the maximum number of teachers
= 8 - 1
= 7
If Jeremy had 7 teachers, the minimum number of packets that Jeremy could possibly give to his classmates
= 14 - 7
= 7
Find out how many packets of notebooks can be distributed to his 15 classmates to have 6 notebooks left.
Number of packets
for classmates |
Total number
of notebooks |
Number of notebooks to
each of his 15 classmates |
|
7
|
7 x 14 =
98 |
98 ÷ 15 =
6 r 8 |
x |
8
|
8 x 14 =
112 |
112 ÷ 15 =
7 r 7 |
x |
9
|
9 x 14 =
126 |
126 ÷ 15 =
8 r 6 |
x |
10
|
10 x 14 =
140 |
140 ÷ 15 =
9 r 5 |
✔ |
(a)
Number of notebooks that each of his 15 classmates received = 9
(b)
Number of packets that Jeremy could give to his 15 classmates = 10
Maximum number of teachers that Jeremy could give one packet each to
= 14 - 10
= 4
Answer(s): (a) 9; (b) 4
