Math Word Problem

Question

Two students took a statistics exam. One of them score 9 points higher than the other and his score was 56% of the sum of their scores.  What are the two scores?

Answer 1

Let the higher score be y.

    y-9  is the other score     [y is "9 points higher than the other"]

 

   y = (56/100)(y + y-9)     [y is "56% of the sum of their scores"; 56% may be written as (56/100)]

 

   100y = 56y + 56y - 504    [multiply by 100; distribute]

    -12y = -504                  [subtract 112y from both sides]

        y = 42                     [divide both sides by (-12)]

        y-9 = 33

 

Answer 2

Scores are x and x + 9

 

x + 9 = 56% of total and x = 44%

Set up a proportion and cross-multiply:

 

x / 44 = (x + 9) / 56

 

56x = 44 (x + 9)

 

56x = 44x + 396

 

12x = 396

x = 33

So the two scores are 33 and 42

33 / (33 + 42) = 0.44

42 / (33 + 42) = 0.56