I need a formula. At a math contest,12 problems were given. Five points were awarded for each correct answer, and two points were deducted for each incorrect answer. Matt's score was 39. How many correct answer did he have
well done
To find the number of correct answers Matt had, we can solve the problem using a system of equations.
Let's assume that x represents the number of correct answers and y represents the number of incorrect answers.
According to the given information, 12 problems were given in total. So we have the equation:
x + y = 12 (Equation 1)
Each correct answer is awarded 5 points, and each incorrect answer has a deduction of 2 points. Matt's score was 39. So we can create the second equation:
5x - 2y = 39 (Equation 2)
Now, we can solve this system of equations to find the values of x and y.
We will use the substitution method to solve the system:
From Equation 1, we can isolate y:
y = 12 - x
Substitute this value of y into Equation 2:
5x - 2(12 - x) = 39
Now, we simplify and solve for x:
5x - 24 + 2x = 39
7x - 24 = 39
7x = 63
x = 9
Now we know that the number of correct answers, x, is 9.
assuming some invisible x's, you are correct.
If he answered all 12 questions, and got x of them correct, then
5x - 2(12-x) = 39
5-2(12-5)=39
5-24+2=39
7=63
9
Am I doing this right