SOLUTION: If one-fourth a number is subtracted from one-half of the number, the difference is 3. Find the number and check your answer. Thank youi very much.

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Question 122802: If one-fourth a number is subtracted from one-half of the number, the difference is 3. Find the number and check your answer.
Thank youi very much.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Let N represent the unknown number.
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One-fourth of N is N divided by 4 which can be written as
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One-half of N is N divided by 2 which can be written as
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If you subtract one-fourth of N from one-half of N this subtraction can be written as:
.

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and the problem tells you that this equals 3. So, in equation form this subtraction is:
.

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You can now put the first term on the left side over a common denominator of 4 by multiplying
it by ... and since this is the same as multiplying the first term
by 1 ... so it does not change the term. This multiplication of the first term by
changes the term to:
.

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and the equation then becomes:
.

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On the left side you combine the two terms by subtracting their numerators and placing the
result over the common denominator. In other words:
.

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and when you substitute this new reduced form of the terms on the left side, the equation becomes:
.

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This equation can be solved for N by multiplying both sides by 4 to get rid of the denominator
on the left side. Multiplying both sides by 4 results in:
.

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So the answer to this problem is that the unknown number N equals 12.
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Check:
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One-half of 12 is 6, and one-fourth of 12 is 3. Then 6 - 3 = 3 which is what the problem says
it should be. So the answer of N = 12 checks.
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Hope this helps you to understand the problem.
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