20 students are in a class. On a test 19 scored and average of 70, how high would last score have to be to raise the average by one point

Question

Please help with steps. I know the answer is 90 but im not sure how they got that. 

Answer 1

The Mean, or Arithmetic Average, is (the sum of the values) divided by (the count of the values).

 

So,

  70 = (T_t+T₂+T₃+T₄+T₅+T₆+T₇+T₈+T₉+T₁₀+T₁₁+T₁₂+T₁₃+T₁₄+T₁₅+T₁₆+T₁₇+T₁₈+T₁₉ ) / 19

 

What value of x is needed so that:

  71 = (T_t+T₂+T₃+T₄+T₅+T₆+T₇+T₈+T₉+T₁₀+T₁₁+T₁₂+T₁₃+T₁₄+T₁₅+T₁₆+T₁₇+T₁₈+T₁₉ + x) / 20 

 

From the first equation,

  T_t+T₂+T₃+T₄+T₅+T₆+T₇+T₈+T₉+T₁₀+T₁₁+T₁₂+T₁₃+T₁₄+T₁₅+T₁₆+T₁₇+T₁₈+T₁₉ = 70*19

            That is, 19 times the average of 70

 

Substituting that into the second equation, we get:

   71 = (70*19 + x) / 20          [once you understand averages, PLZ start here]

 

   71 = (1330 + x) / 20

   1420 = 1330 + x             [multiply both sides by 20]

      90 = x                        [subtract 1330 from both sides]

Answer 2

If the average of 19 students is 70, then the total points (on a 100-point system) is 19 X 70 = 1330 points. For the average to increase to 71, you need 71 X 20 = 1420 points, so that 20th student must score 1420 - 1330 = 90 points.