Question 243748: Please help me in solving this word problem, any and all assistance will be forever appreciated.
Word Problem: The sum of two consecutive integers is 29 less than their product.Find the integers.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! We always want to use the fewest unknowns, which usually means defining as many variables in terms of another variable as possible. Instead of defining two consecutive integers as x & y, define them as x and x+1.
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We are told the sum (x + x+1) is 29 less than the product (x * (x+1)).
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x * (x+1) = x + (x+1) + 29
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x^2 + x = 2x + 30
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Subtracting 2x from both sides
x^2 - x = 30
Subtracting 30 from both sides
x^2 - x - 30 = 0
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We need to determine the factors of 30 that are 1 apart to solve this without using the quadratic equation. We see 5 * 6 = 30 probably will work.
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(x - 6)(x + 5) = 0
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That gives us two values of 'x' to test: x=6 and x=-5.
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Testing x=6.
x = 6
x+1 = 7
Product = 6*7 = 42
Sum = 6+7 = 13
Does 42 = 13 + 29?
Yes. So this solution works.
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Testing x=-5.
x = -5
x+1 =-4
Product = -5*-4 = 20
Sum = -5 + -4 = -9
Are these 29 apart?
Yes, so this checks, too.
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Our solutions are:
5, 6
and
-5,-4
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Done.
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