Multiple choice

The men weight of $150$ students in a certain class is $60\,kg$. The mean weight of boys is $70kg$ and that of girls is $55kg$. What are the number of boys and girls respectively in the class ?

  1. $75$ and $75$
  2. $50$ and $100$
  3. $70$ and $80$
  4. $100$ and $50$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number of boys be b, so the number of girls is 150 - b. Using total weight, 70b + 55(150 - b) = 60(150), which gives b = 50 and 100 girls.

AI explanation

Let the number of boys be B and the number of girls be G; the total number of students is B plus G equals 150. The total weight of the class is 150 multiplied by 60 kg, which equals 9000 kg, and this can also be written using the combined mean formula as 70B plus 55G equals 9000. Dividing the weight equation by 5 gives 14B plus 11G equals 1800. Multiplying the first equation by 11 gives 11B plus 11G equals 1650; subtracting this from the divided weight equation leaves 3B equals 150, so B equals 50. Since there are 150 students in total, G equals 100, meaning there are 50 boys and 100 girls.

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