Ahmad bought fewer than 14 packets of pens. Each packet contained 12 pens. He gave his teachers one packet of pens each before giving an equal number of pens to his 15 schoolmates and had 12 pens left. He had less than 5 teachers.
- How many pens did each of his schoolmates receive?
- What is the maximum number of teachers he could give a packet each to?
Since Ahmad gave one packet of pens each to his teachers, the maximum number of packets that Ahmad could give to his teachers
= 14 - 1
= 13
Since the number of teachers must be less than 5, the maximum number of teachers
= 5 - 1
= 4
If Ahmad had 4 teachers, the minimum number of packets that Ahmad could possibly give to his schoolmates
= 13 - 4
= 9
Find out how many packets of pens can be distributed to his 15 schoolmates to have 12 pens left.
Number of packets for schoolmates |
Total number of pens |
Number of pens to each of his 15 schoolmates |
|
9
|
9 x 12 = 108 |
108 ÷ 15 = 7 r 3 |
x |
10
|
10 x 12 = 120 |
120 ÷ 15 = 8 r 0 |
x |
11
|
11 x 12 = 132 |
132 ÷ 15 = 8 r 12 |
✔ |
(a)
Number of pens that each of his 15 schoolmates received = 8
(b)
Number of packets that Ahmad could give to his 15 schoolmates = 11
Maximum number of teachers that Ahmad could give one packet each to
= 13 - 11
= 2
Answer(s): (a) 8 ; (b) 2