A class has 30-40 students. Each boy in the class bring 15 chocolate bars fcr a class party to celebrate Teacher's Day. The chocolate bars are shared equally among the 20 girls of the class and their form teacher with no leftovers.
There are between 30 and 40 students,
There are 20 girls. Therefore
There are between 10 and 20 boys.
Since each boy brought 15 chocolate bars,
So there are between 150 and 300 chocolate bars, and
therefore, the number of chocolate bars is a multiple of 15.
The chocolate bars are shared equally among 21 people (the girls
and the teacher) with no leftovers.
Therefore the number of bars is also a multiple of 21.
Therefore the number of chocolate bars is a multiple of the
least common multiple of 15 and 21 which is 105. So there
are 105k chocolate bars for some positive integer k, and since
the number of chocolate bars is between 150 and 300,
150 ≦ 105k ≦ 300
Divide all three parts by 105
1.428571429 ≦ k ≦ 2.857142857
So 2 ≦ k ≦ 2
Therefore k = 2
Therefore, there are 105k = 105(2) = 210 chocolate bars.
Since every boy brought 15, there are 210÷15 = 14 boys
Since there are 20 girls and 14 boys, there are
20+14 = 34 students in the class.
Since every girl and the teacher shared the 210 chocolate bars,
every girl and the form teacher received 210÷21 = 10 chocolate
bars.
Solution: 34 students in the class. The form teacher received
10 chocolate bars.
Edwin
