(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Chapter 3.5, Problem 19P

To determine

To show: It is impossible for three consecutive integers to have a sum that is 200 more than the smallest integer.

Expert Solution & Answer

Answer to Problem 19P

The assumption is false

Explanation of Solution

Given information:

To show it is impossible for three consecutive integers to have a sum that is 200 more than the smallest integer.

Let the smallest integer be x .

Then the other two integers will be (x+1),(x+2) .

Let us assume that it is true

According to the question,

x+(x+1)+(x+2)=x+200x+x+x+1+2=x+2003x+3=x+200

Subtract 3x from each side,

3x+3−3x=x+200−3x3=−2x+200or,−2x+200+3

Subtract 200 from each side,

−2x+200−200=3−200−2x=−197

Divide each side by -2

which is not an integer, hence assumption is false

Chapter 3.5, Problem 18P

Chapter 3.5, Problem 20P

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

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