A class has between 30 to 40 students. Each boyin the class brings 15 chocolate bars for a class partyto celebrate Teacher's Day. The chocolate bars areshared equally among the 20 girls of the class andtheir form teacher with no leftovers.How many students are there in the class?
Answers
Answer:
40 students in the class
Step-by-step explanation:
20 boys n 20 girls
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.