SOLUTION: Could someone please help with this problem? "Six-thirteenths of the audiophiles could discriminate between the two products. If 28 of the audiophiles could not discriminate, how

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Question 584623: Could someone please help with this problem?
"Six-thirteenths of the audiophiles could discriminate between the two products. If 28 of the audiophiles could not discriminate, how many could discriminate?"
I came up with 24. Because I figured it would be seven-thirteenths = 28,so I divided 28 by 7 and took that times 6. I don't know if that is right? I am suppose to show how I solved it with an equation but I don't know how to put that into equation form.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer is correct. You basically worked it as a proportion. The critical feature you recognized is that if six-thirteenths could discriminate, then the remaining seven-thirteenths could not. And the problem tells you that 28 could not. So you can establish the following proportion:
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Seven-thirteenths is to 28 as six-thirteenths is to X
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In which X represents the number of audiophiles that could discriminate. In proportion form this can be written as:
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%287%2F13%29%2F28+=+%286%2F13%29%2FX
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This proportion can be solved by cross-multiplying. Multiply the numerator on the left side by the denominator on the right side. Set this equal to the product of the numerator on the right side times the denominator on the left side. In equation form this is:
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%287%2F13%29%2AX+=+%286%2F13%29%2A28
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You can solve this for X by dividing both sides by 7%2F13 which is the multiplier of the X. Remember that if you divide by a fraction, it is the same as inverting the fraction and multiplying. In other words we can multiply both sides of the equation by %2813%2F7%29. This makes the equation become:
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%2813%2F7%29%2A%287%2F13%29%2AX+=+%2813%2F7%29%2A%286%2F13%29%2A28
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On both sides you have a 13 in the numerator that will cancel with a 13 in the denominator as follows:
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and you are left with:
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%287%2F7%29%2AX+=+%286%2F7%29%2A28
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Obviously on the left side you have just X and on the right side you can do exactly what you did ... namely divide 7 into 28 and multiply that result times 6 to get your answer of 24.
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This may help you to see how to do it as an equation, but you did the analysis and math manipulations exactly correct. Good job!!! You knew what you were doing and how to solve this problem. Keep up the good work.
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