Multiple choice

The table shows the number of fillings a class of 40 pupils had at the time of a dental inspection. No. of fillings 0 1 2 3 4 5 6 No. of pupils 1 4 8 x 9 y 2 If the mean number of fillings per pupil is $3.2$, find the values of $ x $ and $y$ .

  1. $x = 5, y = 4$
  2. $x = 10, y = 6$
  3. $x = 9, y = 6$
  4. $x = 12, y = 4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total pupils = 1+4+8+x+9+y+2 = 40, so x+y = 16. Total fillings = (0*1)+(1*4)+(2*8)+(3*x)+(4*9)+(5*y)+(6*2) = 4+16+3x+36+5y+12 = 68+3x+5y. Mean = (68+3x+5y)/40 = 3.2. 68+3x+5y = 128. 3x+5y = 60. Solving x+y=16 and 3x+5y=60: 3x+3y=48, 2y=12, y=6, x=10.