Daniel bought fewer than 13 packets of files. Each packet contained 18 files. He gave his teachers one packet of files each before giving an equal number of files to his 11 classmates and had 8 files left. He had less than 6 teachers.
- How many files did each of his classmates receive?
- What is the maximum number of teachers he could give a packet each to?
Since Daniel gave one packet of files each to his teachers, the maximum number of packets that Daniel could give to his teachers
= 13 - 1
= 12
Since the number of teachers must be less than 6, the maximum number of teachers
= 6 - 1
= 5
If Daniel had 5 teachers, the minimum number of packets that Daniel could possibly give to his classmates
= 12 - 5
= 7
Find out how many packets of files can be distributed to his 11 classmates to have 8 files left.
Number of packets
for classmates |
Total number
of files |
Number of files to
each of his 11 classmates |
|
7
|
7 x 18 =
126 |
126 ÷ 11 =
11 r 5 |
x |
8
|
8 x 18 =
144 |
144 ÷ 11 =
13 r 1 |
x |
9
|
9 x 18 =
162 |
162 ÷ 11 =
14 r 8 |
✔ |
(a)
Number of files that each of his 11 classmates received = 14
(b)
Number of packets that Daniel could give to his 11 classmates = 9
Maximum number of teachers that Daniel could give one packet each to
= 12 - 9
= 3
Answer(s): (a) 14 ; (b) 3
