Mathematics Dictionary
Dr. K. G. Shih
Indefinite Equations
Subjects
Symbol Defintion
Example : x^2 = square of x
AL 19 00 |
- Outlines
AL 19 01 |
- Definition of in-definite equations<
AL 19 02 |
- Example : 100 people and 100 cakes
AL 19 03 |
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AL 19 04 |
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AL 19 05 |
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AL 19 06 |
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AL 19 07 |
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AL 19 08 |
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AL 19 09 |
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AL 19 10 |
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Answers
AL 19 01. Definition of indefinite equations Definitin
1. Two varibles and one equation
2. Three varibles and two equations
Example : Solve x + y = 101 for x and y between 50 and 55
x = 49 and y = 52 Not solution
x = 50 and y = 51 Solution
x = 51 and y = 50 Solution
x = 52 and y = 49 Not solution
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AL 19 02. One hundred people and one hundred cakes
Question
One hundred people include men, women and children
For man : each man has 3 cakes
For women : each women has two cakes
For children : each three children has one cake
How many men, women and children ?
Solution
Let x = men, y = women and z = children
Equations
x + y + z = 100 ......... (1)
3*x + 2*y + z/3 = 100 ... (2)
Solve equations
3*(2) : 9*x + 6*y + z = 300 .... (3)
(3) - (1) : 8*x + 5*y = 200
Hence y = (200 - 8*x)/5 and x must be multiple of 5
x = 05, y = 32 and z = 63
x = 10, y = 24 and z = 66
x = 15, y = 16 and z = 69
x = 20, y = 08 and z = 72
Verify
3*05 + 2*32 + 63/3 = 15 + 64 + 21 = 100
3*10 + 2*24 + 66/3 = 30 + 48 + 22 = 100
3*15 + 2*16 + 69/3 = 45 + 32 + 23 = 100
3*20 + 2*08 + 72/3 = 60 + 16 + 24 = 100
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AL 19 03
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AL 19 04.
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AL 19 05.
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AL 19 06.
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AL 19 07.
Method
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AL 19 08.
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AL 19 09. Answer
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AL 19 10. Answer
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AL 19 00. Outlines
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