Problema Solution
Miguel scored 5 points higher on his midterm and 13 points higher on his final examination than he did on his first examination. If his mean (average) score was 90, find his score on his first examination
Answer provided by our tutors
let
x = the score on the first examination
y = the score on the midterm
z = the score on the final examination
Miguel scored 5 points higher on his midterm than he did on his first examination
y = x + 5
Miguel scored 13 points higher on his final examination than he did on his first examination
z = x + 13
his mean (average) score was 90
(x + y + z)/3 = 90
by solving the system of equations
y = x + 5
z = x + 13
(x + y + z)/3 = 90
we find
x = 84 points
y = 89 points
z = 97 points
Miguel's score on his first examination was 84 points.