Francine and Cheryl received equal scores on a test made up of multiple choice questions and an essay. Francine got 34 multiple choice questions correct and received 14 points for her essay. Cheryl got 30 multiple choice questions correct and received 22 points for her essay.
How many points was each multiple choice question worth?
Let's assume each multiple choice question is worth x points.
Since Francine got 34 multiple-choice questions correct, the total number of points she got from the multiple-choice questions is 34x.
Since Cheryl got 30 multiple-choice questions correct, the total number of points she got from the multiple-choice questions is 30x.
Each received equal scores on the test, so 34x + 14 = 30x + 22.
Combining like terms, we get 4x + 14 = 22.
Subtracting 14 from both sides, we get 4x = 8.
Dividing both sides by 4, we get x = 2.
So, each multiple-choice question is worth 2 points. Answer: \boxed{2}.
To find out how many points each multiple choice question was worth, we need to subtract the points received for the essay from the total score and then divide it by the number of multiple choice questions answered correctly.
Let's calculate it step by step:
1. Francine received 34 points for the multiple choice questions and 14 points for the essay. So her total score is 34 + 14 = 48.
2. Cheryl received 30 points for the multiple choice questions and 22 points for the essay. So her total score is 30 + 22 = 52.
3. Since both Francine and Cheryl received equal scores on the test, we can set their total scores equal to each other:
48 = 52
4. Subtracting 48 from both sides of the equation gives us:
52 - 48 = 0
5. Simplifying the equation, we have:
4 = 0
6. However, this is not possible, as 4 cannot equal 0.
Based on this calculation, it seems there may be an error in the given information or an inconsistency in the scoring system. Please double-check the details provided.
To find out how many points each multiple-choice question is worth, we need to determine the total number of points earned by both Francine and Cheryl and then divide that total by the total number of multiple-choice questions they both answered correctly.
Let's calculate their total scores first:
Francine's total score = Number of correct multiple-choice questions + Points for essay
= 34 + 14
= 48
Cheryl's total score = Number of correct multiple-choice questions + Points for essay
= 30 + 22
= 52
We can see that both Francine and Cheryl received equal scores, so their total scores are the same.
Now, we can calculate the value of each multiple-choice question by dividing their total scores by the number of multiple-choice questions answered correctly:
Value of each multiple-choice question = Total score / Number of correct multiple-choice questions
For Francine:
Value of each multiple-choice question = Francine's total score / Number of correct multiple-choice questions Francine answered
= 48 / 34
≈ 1.4118
For Cheryl:
Value of each multiple-choice question = Cheryl's total score / Number of correct multiple-choice questions Cheryl answered
= 52 / 30
≈ 1.7333
So, each multiple-choice question is worth approximately 1.4118 points for Francine and 1.7333 points for Cheryl.