in a math contest of 20 problems. 5 hpoints given each correct answer. 25 points are deducted for each incorrect answer. if janelle answered 20 problems and scored 72 points. how many correct answers did she had?
Since each question scores a multiple of 5 points, how do you wind up with a score of 72?
To find out how many correct answers Janelle had, we can set up an equation using the given information.
Let's denote the number of correct answers as C and the number of incorrect answers as I.
Since Janelle answered all 20 problems, we know:
C + I = 20 (Equation 1)
We also know that she scored 72 points. For each correct answer, she gets 5 points, so the total points for correct answers is 5C. And for each incorrect answer, she loses 25 points, so the total points deducted for incorrect answers is 25I.
Based on this, we can write another equation:
5C - 25I = 72 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (C and I).
We can solve this system of equations to find the values of C and I.
Multiplying Equation 1 by 25, we get:
25C + 25I = 500 (Equation 3)
Adding Equation 2 and Equation 3, we eliminate the variable I:
25C + 25I + 5C - 25I = 500 + 72
Simplifying, we get:
30C = 572
Dividing both sides by 30:
C = 19.07
Since C represents the number of correct answers, it must be a whole number. Therefore, Janelle answered 19 correct questions.
So, Janelle had 19 correct answers.