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Question 249475: the sum of 2 consecutive integers is 27 more than 5 times the larger integer find the integers
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! We always seek ways to use the fewest unknowns when solving word problems.
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We could call the two integers 'x' and 'y'. But we are told they are consecutive, so we can say:
x = x
y = x+1
That gives us only one unknown, 'x'.
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We also are given some relationships:
the sum of two consecutive integers: x + x+1
is 27 more than 5 times the larger integer: 5(x+1) + 27
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So,
x + x+1 = 5(x+1) + 27
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Collecting and simplifying terms
2x + 1 = 5x + 5 + 27
2x + 1 = 5x + 32
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Subtracting 1 from both sides
2x = 5x + 31
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Subtracting 5x from both sides
-3x = 31
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Dividing both sides by -3 shows that 'x' is NOT an integer, so there is no solution...
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If only the setup had been 26 more instead of 27. (Or is that a typo?)
Then we would have had:
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2x + 1 = 5x + 5 + 26
2x + 1 = 5x + 31
2x = 5x + 30
-3x = 30
x = -10
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Then the two consecutive integers would have been: -10 and -9.
-10 + (-9) = -19
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5*(-9) = -45
-45 + 26 = -19
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Done.
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