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The sum of an integer and 3 times the next consecutive integer is 27 . Find the value of the lesser integer. Answer:

The sum of an integer and 33 times the next consecutive integer is 2727 . Find the value of the lesser integer.\newlineAnswer:

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Full solution

Q. The sum of an integer and 33 times the next consecutive integer is 2727 . Find the value of the lesser integer.\newlineAnswer:
  1. Denote integers: Let's denote the lesser integer as xx. The next consecutive integer is x+1x + 1. According to the problem, the sum of the lesser integer and three times the next consecutive integer is 2727. We can write this as an equation:\newlinex+3(x+1)=27x + 3(x + 1) = 27
  2. Write equation: Now, let's distribute the 33 to both terms inside the parentheses: x+3x+3=27x + 3x + 3 = 27
  3. Distribute 33: Combine like terms on the left side of the equation:\newline4x+3=274x + 3 = 27
  4. Combine like terms: Subtract 33 from both sides of the equation to isolate the term with xx: \newline4x+3−3=27−34x + 3 - 3 = 27 - 3\newline4x=244x = 24
  5. Isolate xx: Divide both sides of the equation by 44 to solve for xx:4x4=244\frac{4x}{4} = \frac{24}{4}x=6x = 6

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