Question

A class has 30-40 students. Each boy in the class bring 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?
Detailed steps please!

Answer 1

Answer:

There 30 - 40 students altogether

There are 20 girls.

There are 10 - 20 boys.

Therefore if each boy brings 15 chocolate bars, there are between 150 and 300 chocolate bars, and

the number of chocolate bars is a multiple of 15.

The chocolate bars are shared among 21 people (the girls

and the teacher).

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.

Answer 2

9514 1404 393

Answer:

  34

Step-by-step explanation:

In order to divide some multiple of 15 chocolate bars evenly by 21, the number of bars must be a multiple of the LCM of 15 and 21, which is 105. That number is 7 times 15, indicating the number of boys in the class must be a multiple of 7. The only number between 30-20 = 10 and 40-20 = 20 that is a multiple of 7 is 14.

There must be 14 boys in the class, so 34 students in total.

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The boys brought a total of 210 chocolate bars, so each girl and the teacher received 10 of them.