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?
x + y =20
5x -1y =70
x = # correct y + # wrong.
add the two equations together since the y's will cancel.
6x = 90
x = 15 correct
how many are wrong?
To solve this problem, let's use some algebra. Let's say the number of correct answers is C and the number of incorrect answers is I.
According to the information given, the teacher gives you 5 points for each correct answer and takes away 1 point for each incorrect answer. So, the total score can be calculated using the following equation:
Total score = 5C - I
We are also given that the total score is 70. Substituting this value into the equation, we get:
70 = 5C - I
Now, we need to think about the number of questions on the test. The question states that there are 20 questions in total. Therefore, the total number of answers given can be represented as:
Total answers = C + I
Substituting this value into the previous equation, we get:
70 = 5C - (Total answers - C)
Simplifying the equation further, we get:
70 = 6C - Total answers
Since the number of total answers is equal to 20, we can substitute this value into the equation:
70 = 6C - 20
Adding 20 to both sides of the equation, we get:
90 = 6C
Dividing both sides of the equation by 6, we find:
C = 15
Therefore, you got 15 questions correct on the test.
To solve this problem, we can use a method called algebraic reasoning. Let's assume the number of correct answers is represented by "x".
Given that you receive five points for each correct answer and one point is deducted for each incorrect answer, we can create an equation to represent your score on the test.
The equation is:
5x - (20 - x) = 70
Let's break it down. There are 20 questions in total on the test. You receive 5 points for each correct answer, so the total points earned from correct answers is 5x. For incorrect answers, one point is deducted for each incorrect answer. Since there are 20 questions in total, the number of incorrect answers can be calculated by subtracting the number of correct answers (x) from the total number of questions (20-x).
Simplifying the equation, we have:
5x - (20 - x) = 70
Expanding the brackets:
5x - 20 + x = 70
Combining like terms:
6x - 20 = 70
Adding 20 to both sides:
6x = 90
Dividing both sides by 6:
x = 15
Therefore, you got 15 questions correct on the test.