Multiple choice

Directions: Solve the following question and mark the best possible option. A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is

  1. 9.5

  2. 10

  3. 4.5

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B_avg and G_avg be the initial averages. Total initial sum = 20*B_avg + 30*G_avg. Given G_avg = B_avg + 5. Final sum = 20*(B_avg + x) + 30*(G_avg - 3). The final class average increased by 2, so final sum = 50*( (20*B_avg + 30*G_avg)/50 + 2 ). Solving for x gives 9.5.

AI explanation

The class has 20 boys and 30 girls, so if the boys' average score is x, the girls' average score is x + 5, making the initial overall average (20x + 30(x + 5)) divided by 50, which simplifies to x + 3. In the final exam, the girls' average drops by 3 to become x + 2, and the overall class average increases by 2 to become x + 5. Let the boys' final average be y, so the final equation is (20y + 30(x + 2)) divided by 50 equals x + 5. Solving 20y + 30x + 60 = 50x + 250 gives 20y = 20x + 190, meaning y = x + 9.5, so the increase in the boys' average is 9.5.

Keep practicing — related questions