Question

Two students took a test. one of them scored 9 points higher than the other and his score was 56% of the sum of their scores. a score is between the value of 0 - 100, inclusive. what were the scores obtained for each of them?

Answer 1

Let x and y be the points scored by the two students. Then,
x = y+9

However,
x = 56%(x+y)= 0.56(x+y)

But, y = x-9
Therefore,
x = 0.56(x+x-9) = 0.56(2x-9) = 1.12x - 5.04
(1.12-1)x = 5.04
0.12x = 5.04
x = 42 points
And
y = x-9 = 42-9 = 33 points

Therefore, scores obtained by each are 42 and 33 points.