Warren bought fewer than 15 packets of files. Each packet contained 12 files. He gave his teachers one packet of files each before giving an equal number of files to his 7 schoolmates and had 4 files left. He had less than 4 teachers.
- How many files did each of his schoolmates receive?
- What is the maximum number of teachers he could give a packet each to?
Since Warren gave one packet of files each to his teachers, the maximum number of packets that Warren could give to his teachers
= 15 - 1
= 14
Since the number of teachers must be less than 4, the maximum number of teachers
= 4 - 1
= 3
If Warren had 3 teachers, the minimum number of packets that Warren could possibly give to his schoolmates
= 14 - 3
= 11
Find out how many packets of files can be distributed to his 7 schoolmates to have 2 files left.
Number of packets
for schoolmates |
Total number
of files |
Number of files to
each of his 7 schoolmates |
|
11
|
11 x 12 =
132 |
132 ÷ 7 =
18 r 6 |
x |
12
|
12 x 12 =
144 |
144 ÷ 7 =
20 r 4 |
✔ |
(a)
Number of files that each of his 7 schoolmates received = 20
(b)
Number of packets that Warren could give to his 7 schoolmates = 12
Maximum number of teachers that Warren could give one packet each to
= 14 - 12
= 2
Answer(s): (a) 22 ; (b) 2
