Question

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?

Answer 1

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}.