# math

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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?

• math -

number correct --- x
number incorrect --- y
number skipped ---- 25 - x - y

4x - y + 0(25-x-y) = 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

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