math
posted by sarah on .
a quiz has 25 questions with 4points awarded for each correct answer and 1 point deducted for each incorrect answer,with zero for each question omitted.John scores 77points.how many questions did he omit?

number correct  x
number incorrect  y
number skipped  25  x  y
4x  y + 0(25xy) = 77
4x  y = 77
y = 4x  77
so 4x  77 ≥ 0 and we also know x+y ≤ 25
4x ≥ 77
x ≥ 77/4 , but x must be an integer
so x ≥20
so we could have
x y (s)kipped
20 3 2
21 7 2 > invalid
22 11 8 > invalide
etc
the only one that will work is
correct 20
wrong 3
skipped 2