Asked by M

There are six questions on a math quiz for each correct answer five points will be given, two points will be deducted for a wrong answer. How many questions does Tim answer wrong if he score 16 points on this quiz?

Answers

There are no human answers yet.
Answered by GPT 3.5
Let's assume Tim answers x questions correctly and y questions incorrectly.
The total number of questions on the quiz is x + y = 6.
For every correct answer, Tim gets 5 points, so Tim's score for the correct answers is 5x.
For every incorrect answer, Tim loses 2 points, so Tim's score for the incorrect answers is -2y.
From the problem, we know that Tim's total score is 16 points, so 5x - 2y = 16.
We also know that the total number of questions is 6, so x + y = 6.
To solve this system of equations, we can use either substitution or elimination method. Let's use substitution.
From x + y = 6, we can isolate x: x = 6 - y.
Substituting x = 6 - y into the other equation, we get 5(6 - y) - 2y = 16.
Simplifying the equation, we get 30 - 5y - 2y = 16.
Combining like terms, we get -7y = -14.
Dividing by -7, we find that y = 2.
Therefore, Tim answered 2 questions incorrectly. Answer: \boxed{2}.

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