A quiz has 20 questions with 5 points awarded for each correct answer and one point deducted for each incorrect answer, with 0 for each question omitted, Larry scored 72 points. How many questions did he omit?

Answer 1

number correct --- x , 0 ≤ x ≤ 20
number wrong ---- y
number skipped ---- 20-x-y

5x - y + 0 = 72

y = 5x - 72
y ≥ 0

if x = 14, y = -2 , not possible
if x = 15 , y = 3 , skipped = 2
if x = 16, y = 8 , not possible , x+y>20

so he got 16 right, 8 wrong, and skipped 2

check:
5(16) - 1(8) + 0 = 72