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How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer? Use the method shown in Example 9.6.5 to answer this question. Start by thinking of the number 21 as divided into 21 individual items and the variables X₁, X₂, and x3 as three categories into which these items are placed. Since each x; is a ---Select--- integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is

How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer? Use the method shown in Example 9.6.5 to answer this question. Start by thinking of the number 21 as divided into 21 individual items and the variables X₁, X₂, and x3 as three categories into which these items are placed. Since each x; is a ---Select--- integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
Problem 14OE
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How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer? Use the method shown in Example 9.6.5 to answer this question. Start by thinking of the number 21 as divided into 21 individual items and the variables X₁, X2, and x3 as three categories into which these items are placed. Since each x; is a -Select--- integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is
Transcribed Image Text:How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer? Use the method shown in Example 9.6.5 to answer this question. Start by thinking of the number 21 as divided into 21 individual items and the variables X₁, X2, and x3 as three categories into which these items are placed. Since each x; is a -Select--- integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is
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