Multiple choice

The average (arithmetic mean) of all the grades on a certain algebra test was $90$. If the average of the $8$ males grades was $87$, and the average of the females grades was $92$, calculate the number of female students.

  1. 8

  2. 9

  3. 10

  4. 11

  5. 12
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let m be the number of males (8) and f be the number of females. Total average = (8*87 + f*92) / (8+f) = 90. 696 + 92f = 90(8+f). 696 + 92f = 720 + 90f. 2f = 24. f = 12.

AI explanation

Let the number of female students be F. The sum of all grades is 90 multiplied by (8 plus F), which equals the sum of the boys' grades (8 multiplied by 87) plus the girls' grades (92 multiplied by F). This gives the equation 720 plus 90F equals 696 plus 92F. Solving for F gives 2F equals 24, making the result 12 female students.

Keep practicing — related questions