On a 20 question math test, your teacher gives you five points for every correct answer and takes away one point for each incorrect answer. If you score 70 on the test, how many did you get correct?

Question

On a 20 question math test, your teacher gives you five points for every correct answer and takes away one point for each incorrect answer. If you score 70 on the test, how many did you get correct?

Answer 1

the answer is 15 because 15*5=75 75-5 ( the 5 you got wrong) = 70

Answer 2

number correct --- x

number incorrect --- 20-x

5x -1(20-x) = 70
5x - 20 + x = 70
6x = 90
x = 90/6 = 15 , as Bob stated

Answer 3

Let's start by assigning variables to the unknown quantities in the problem.

Let x be the number of correct answers.
Let y be the number of incorrect answers.

Based on the given information, we can create two equations:

Equation 1: x + y = 20 (since there are 20 questions in total)

Equation 2: 5x - y = 70 (since for each correct answer you get 5 points and each incorrect answer costs you 1 point, resulting in a total score of 70)

To solve this system of equations, we can use the substitution method or elimination method. Let's use the elimination method:

Multiply Equation 1 by 5 to make the coefficients of y the same:

5x + 5y = 100

Now, add Equation 2 to this modified Equation 1:

5x + 5y + 5x - y = 100 + 70

This simplifies to:

10x + 4y = 170

Now, divide this equation by 2 to simplify further:

5x + 2y = 85

Now we have a new equation:

Equation 3: 5x + 2y = 85

Let's solve Equation 3 and Equation 1 simultaneously:

Multiply Equation 1 by 2 to make the coefficients of y the same:

2x + 2y = 40

Now, subtract Equation 1 from this modified Equation 3:

(5x + 2y) - (2x + 2y) = 85 - 40

This simplifies to:

3x = 45

Divide both sides of the equation by 3:

x = 15

So, you got 15 questions correct on the test.

Answer 4

To solve this problem, we can start by letting the number of correct answers be represented by 'x'. Since each correct answer is worth 5 points, the total points from correct answers can be calculated as 5*x.

Next, we need to consider the number of incorrect answers. Since each incorrect answer leads to a deduction of 1 point, the total points lost from incorrect answers can be calculated as 1*(20-x) since there are 20 questions in total.
Based on the information given, the total score is 70 points. So we can set up the equation: 5x - (20-x) = 70.
Simplifying the equation gives us: 5x - 20 + x = 70.
Combining like terms gives us: 6x - 20 = 70.
Adding 20 to both sides of the equation gives us: 6x = 90.
Finally, dividing both sides of the equation by 6 gives us: x = 15.
Therefore, you answered 15 questions correctly on the math test.