SOLUTION: The sum of two even numbers is 30. the larger number is twelve more than one half the smaller number . find the numberS

Question 573617: The sum of two even numbers is 30. the larger number is twelve more than one half the smaller number . find the numberS
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let's call the smaller number S. And let's call the larger number L.
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The problem tells you that the sum of the smaller number, S, and the larger number, L, equals 30. So we can write the equation:
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S + L = 30
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Next the problem says that the larger number (L) is twelve more than one half the smaller number (S).
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One half the smaller number is S divided by 2 which is S/2. 12 more than that is:
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S/2 + 12
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and this equals the larger number. So we can write another equation:
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S/2 + 12 = L
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Now we have two independent equations so we can solve for the two unknowns. The equations are:
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S + L = 30 and
S/2 + 12 = L
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Since the second equation says that L = S/2 + 12, we can substitute the right hand side of this equation for the L that appears in the first equation we wrote above. Making this substitution makes the first equation become:
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S + S/2 + 12 = 30
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Eliminate the +12 on the left side by subtracting 12 from both sides to get:
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S + S/2 = 18
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Next, add the two terms on the left side as follows:
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S + S/2 = 2S/2 + S/2 = 3S/2
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(Note that S = 2S/2 gives both terms the common denominator of 2, so the two terms can be added by adding their numerators and putting that result over the common denominator 2.)
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Replace the S + S/2 with its equivalent 3S/2 and the equation becomes:
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3S/2 = 18
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Get rid of the denominator 2 by multiplying both sides of this equation by 2 to get:
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3S = 36
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Solve for S by dividing both sides by 3 and you have:
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S = 12
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Now we know that the smaller number is the even number 12. And since the sum of the two numbers is 30 we also know that the larger number must be 18 (because 18 + 12 = 30) which is also an even number.
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You can check this problem by ensuring that the larger number (18) is 12 more than half the smaller (half of 12). Since 18 is 12 more than 6, this checks. Therefore, we know that this answer is correct ... namely the smaller even number is 12 and the larger even number is 18.
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Hope this explanation helps you to understand the problem a little better.
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