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?
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}.
Let's assume that Tim answers x questions correctly and y questions incorrectly.
For each correct answer, Tim earns 5 points. Therefore, the total points earned for the correct answers would be 5x.
For each wrong answer, Tim loses 2 points. Therefore, the total points deducted for the wrong answers would be 2y.
Given that the total score is 16 points, we can write the equation as follows:
5x - 2y = 16
To find the number of questions Tim answered wrong, we need to solve for y.
Let's solve the equation:
5x - 2y = 16
Rearranging the equation:
-2y = 16 - 5x
Divide both sides by -2:
y = (16 - 5x) / -2
Since we are looking for the number of questions answered wrongly, y should be a non-negative integer.
Let's find the possible values of x for which y is a whole number.
If we substitute x = 0, we have:
y = (16 - 5(0)) / -2
y = 16 / -2 = -8
Since y cannot be negative, x = 0 does not give us a valid solution.
If we substitute x = 1, we have:
y = (16 - 5(1)) / -2
y = (16 - 5) / -2
y = 11 / -2 = -5.5
Again, y cannot be negative, so x = 1 does not give us a valid solution either.
If we substitute x = 2, we have:
y = (16 - 5(2)) / -2
y = (16 - 10) / -2
y = 6 / -2 = -3
As y cannot be negative, x = 2 does not give us a valid solution.
If we substitute x = 3, we have:
y = (16 - 5(3)) / -2
y = (16 - 15) / -2
y = 1 / -2 = -0.5
Once again, y cannot be negative, so x = 3 does not give us a valid solution.
Continuing this process, we find that there are no integer values of x for which y is a whole number. This means that Tim cannot score 16 points on this quiz.
Therefore, it is not possible to determine how many questions Tim answers wrong to score 16 points on the quiz.
To solve this problem, we need to set up an equation based on the information given. Let's assume that the number of correct answers is x.
Since each correct answer is worth 5 points, the total points earned from correct answers is 5x.
Since each wrong answer deducts 2 points, the total points deducted from wrong answers is 2(6 - x) or 12 - 2x.
Given that Tim scored 16 points, we can set up the equation:
5x - (12 - 2x) = 16
Now, let's solve this equation to find the value of x.
5x - 12 + 2x = 16
Combine like terms:
7x - 12 = 16
Add 12 to both sides:
7x = 28
Divide both sides by 7:
x = 4
Therefore, Tim answered 4 questions correctly.
Now, to find the number of questions Tim answered wrong, we subtract the number of correct answers from the total number of questions:
Number of questions answered wrong = Total number of questions - Number of correct answers
Number of questions answered wrong = 6 - 4
Number of questions answered wrong = 2
Therefore, Tim answered 2 questions incorrectly.