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Question 108952This question is from textbook Harcourt Math Practice Workbook
: Two numbers have a difference of 10 and the sum of 34. What are the numbers?
This question is from textbook Harcourt Math Practice Workbook
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Call the two unknown numbers x and y.
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Since their difference is 10 you can write the equation:
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x - y = 10
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And since their sum is 34 you can write the equation:
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x + y = 34
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Write the two equations one above the other:
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x - y = 10
x + y = 34
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Note that if you add the two equations vertically in columns that the -y of the top equation
will cancel the +y of the bottom equation. So, adding vertically results in the x + x = 2x,
the two y terms cancel, and on the right side the 10 + 34 = 44
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Therefore, the result of the addition is:
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2x = 44
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And if you divide both sides of this equation by 2 you get:
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x = 22
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Since x + y is to equal 34, then you can write:
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22 + y = 34
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Subtracting 22 from both sides of this equation results in:
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y = 12
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So the answer to this problem is that one of the numbers is 22 and the other is 12.
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As a check, note that the difference of the two numbers is 22 - 12 = 10 and the sum of the
two numbers is 22 + 12 = 34, just as the problem says things should be.
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Hope this helps you to understand the problem a little better.
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