Louann and Carla received equal scores on a test made up of multiple choice questions and an essay. Louann got 14 multiple choice questions correct and received 24 points for her essay. Carla got 16 multiple choice questions correct and received 14 points for her essay.
How many points was each multiple choice question worth?
da answer is 5
To find out how many points each multiple choice question was worth, we need to divide the total number of points earned in the multiple choice section by the number of correct multiple choice questions.
For Louann:
She got 14 multiple choice questions correct and the total number of points earned in the multiple choice section is unknown.
For Carla:
She got 16 multiple choice questions correct and the total number of points earned in the multiple choice section is unknown.
Since both Louann and Carla received equal scores on the test, we can set up an equation:
14x + 24 = 16x + 14
Where x represents the number of points each multiple choice question is worth.
Let's solve the equation:
24 - 14 = 16x - 14x
10 = 2x
x = 5
Therefore, each multiple choice question is worth 5 points.
To find out how many points each multiple choice question is worth, we need to divide the total points for the multiple choice questions by the number of questions answered correctly by either Louann or Carla.
Louann answered 14 multiple choice questions correctly and Carla answered 16 multiple choice questions correctly. Therefore, the total number of multiple choice questions answered correctly is 14 + 16 = 30.
Now, we need to calculate the total points for the multiple choice questions answered correctly. Since both Louann and Carla received equal scores on the test, we can use either Louann's or Carla's multiple choice score.
If we use Louann's score, she received 24 points for her essay. So, if we subtract the essay points from the total score, we get the total points for the multiple choice questions.
Total multiple choice points = Total score - Essay points
Total multiple choice points = Total score - 24
Since we don't know the total score, we can use an algebraic equation to represent it. Let's assume each multiple choice question is worth x points.
Total score = (Number of multiple choice questions) * (Points per question)
Total score = 30x
Now we can substitute this expression for the total score into the equation for the total multiple choice points.
Total multiple choice points = 30x - 24
Since Louann got 14 multiple choice questions correct, we can set up another equation using her score.
Total multiple choice points = (Number of questions Louann answered correctly) * (Points per question)
30x - 24 = 14x
To isolate x (the points per question), we need to solve this equation for x.
30x - 24 = 14x
16x = 24
x = 24/16
x = 1.5
Therefore, each multiple choice question is worth 1.5 points.