Question

13. A class has between 30 to 40 students. Each boy
in the class brings 15 chocolate bars for 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.
(i) How many students are there in the class?
(ii) How many chocolate bars does their form
teacher receive​

Answer 1

Answer:

34 students in the class and the form teacher received  10 chocolate bars.

Step-by-step explanation:

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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.