Xavier bought fewer than 15 packets of notebooks. Each packet contained 20 notebooks. He gave his teachers one packet of notebooks each before giving an equal number of notebooks to his 14 friends and had 2 notebooks left. He had less than 4 teachers.
- How many notebooks did each of his friends receive?
- What is the maximum number of teachers he could give a packet each to?
Since Xavier gave one packet of notebooks each to his teachers, the maximum number of packets that Xavier 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 Xavier had 3 teachers, the minimum number of packets that Xavier could possibly give to his friends
= 14 - 3
= 11
Find out how many packets of notebooks can be distributed to his 14 friends to have 8 notebooks left.
Number of packets
for friends |
Total number
of notebooks |
Number of notebooks to
each of his 14 friends |
|
11
|
11 x 20 =
220 |
220 ÷ 14 =
15 r 10 |
x |
12
|
12 x 20 =
240 |
240 ÷ 14 =
17 r 2 |
✔ |
(a)
Number of notebooks that each of his 14 friends received = 17
(b)
Number of packets that Xavier could give to his 14 friends = 12
Maximum number of teachers that Xavier could give one packet each to
= 14 - 12
= 2
Answer(s): (a) 18 ; (b) 2
