Question 516011: a student missed 6 questions and received 87% if all the problems where equal value how many problems where on the test
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The exam has an unknown number of questions. Let's call that number x.
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The student misses 6 questions. That means that the number of questions that the student got correct was x - 6. If you divide the number that the student answered correctly by the total number of questions, you should get the score of 87% or 0.87.
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In equation form, the numerator is the number correctly answered (x - 6) and the denominator is the total number of questions (x) and that division should result in an answer of 0.87. In equation form this is:
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To get rid of the denominator, multiply both sides of the equation by x. On the left side, the x multiplier cancels with the x denominator, and the left side becomes just the numerator of x - 6. On the right side the multiplication results in the product of 0.87 times x. Therefore, the after multiplying both sides of the equation by x and simplifying the equation is:
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Cancel the minus 6 on the left side by adding +6 to both sides. The result is:
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Subtract 0.87x from both sides. On the left side, taking 0.87x from x results in 0.13x. On the right side, this subtraction cancels the 0.87x. The equation has now become:
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Solve for x by dividing both sides by 0.13 and the result is:
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The division on the right side results in 46.1538
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Since the decimal part of this answer (that is, the 0.1538) doesn't make sense (what does 0.1538 of a question mean?) just round off the answer to 46 questions.
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That means that by missing 6 questions, the student got 40 of 46 correct. If you divide 40 by 46 you would find that the student got a score of 86.956% which the teacher rounded to 87%. That checks our answer.
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The answer to this problem is that the exam had a total of 46 questions.
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Hope this helps you to understand the problem.
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