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30 Sep 2019, 18:40
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63%
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based on 27
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Find the number of non-negative integer solutions for \(x+3y+8z=20\).
A. 12
B. 13
C. 14
D. 15
E. 16
A. 12
B. 13
C. 14
D. 15
E. 16
Archived Topic
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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30 Sep 2019, 22:56
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x+3y+8z=20
As, we have to find non-negative integral solutions, z can take only 3 values, that is 0, 1 or 2.
Case 1- If z=0
x+3y+0=20
3y=20-x
20=2 mod 3
x must be 2 mod 3
x=3k+2, less than or equal to 20
k or x can take 7 values
Case 2- If z=1
x+3y+8=20
3y=12-x
As 3y and 12 are both multiple of 3, x must be a multiple of 3.
x=3a, less than or equal to 12
a or x can take 5 values
Case 3- z=2
x+3y+16=20
3y= 4-x
x can take 2 values.
Total number of non-negative integer solutions= 7+5+2=14
As, we have to find non-negative integral solutions, z can take only 3 values, that is 0, 1 or 2.
Case 1- If z=0
x+3y+0=20
3y=20-x
20=2 mod 3
x must be 2 mod 3
x=3k+2, less than or equal to 20
k or x can take 7 values
Case 2- If z=1
x+3y+8=20
3y=12-x
As 3y and 12 are both multiple of 3, x must be a multiple of 3.
x=3a, less than or equal to 12
a or x can take 5 values
Case 3- z=2
x+3y+16=20
3y= 4-x
x can take 2 values.
Total number of non-negative integer solutions= 7+5+2=14
TheNightKing
Find the number of non-negative integer solutions for \(x+3y+8z=20\).
A. 12
B. 13
C. 14
D. 15
E. 16
A. 12
B. 13
C. 14
D. 15
E. 16
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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