The contestant answered 13 questions correctly, and 7 were incorrectly answered.
Work Step by Step
Let x = the number of correct answers y = the number of incorrect answers A contestant on a quiz show gets 150 points for every correct answer and loses 250 points for each incorrect answer. The contestant completed 20 questions. Hence, we get the system of equations: $x+y=20$ $150x-250y=200$ The first equation will be: $y=20-x$ Write the second equation. Substitute 10x + 50 for y. $150x-250(20-x)=200$ $150x-5000+250x=200$ $400x=5200$ $x=13$ Solve for $y$: $13+y=20$ $y=7$ The contestant answered 13 questions correctly, and 7 were incorrectly answered.