Explanation Method: The method of solving the system of equations by substitution method is used through the following steps. 1. Define the variables. 2. Frame the equations. 3. Isolate each equation for one variable. 4. Substitute one variable value to determine the values of other two variables. Calculation: Consider the provided information that a man buys 100 birds for $ 100 and he buys at least one of each type. The cost of rooster is $ 10 , a hen is $ 3 and pair of chicks is $ 1 . Define the variables as: x = number of roosters y = number of hens z = number of chicks As the man buys 100 birds, the first equation is: x + y + z = 100 As the man buys 100 birds for $ 100 with each of its cost, the second equation is: 10 x + 3 y + 1 2 z = 100 This equation can be written as, z = 200 − 20 x − 6 y Substitute this obtained z = 200 − 20 x − 6 y in the first equation. x + y + 200 − 20 x − 6 y = 100 − 19 x − 5 y = − 100 19 x + 5 y = 100 y = − 19 5 x + 20 As the number of each bird must be whole numbers, x must be a multiple of 5 in order to cancel out the denominator in the coefficient

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities.…

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Chapter 5.7, Problem 58PS

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The number of roosters, hens and chicks bought by a man for $100 if he buys 100 birds with each rooster costing $10, a hen costing $3 and pair of chicks costing $1 and he buys at least one of each type.

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Chapter 5.7, Problem 57PS

Chapter 5.7, Problem 59PS

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Chapter 5 Solutions

Nature of Mathematics (MindTap Course List)

Ch. 5.1 - Level 1 IN YOUR OWN WORDS Explain each of the...Ch. 5.1 - Prob. 2PS Ch. 5.1 - Prob. 3PS Ch. 5.1 - Prob. 4PS Ch. 5.1 - Prob. 5PS Ch. 5.1 - Prob. 6PS Ch. 5.1 - Prob. 7PS Ch. 5.1 - Prob. 8PS Ch. 5.1 - Prob. 9PS Ch. 5.1 - Prob. 10PS

Ch. 5.1 - Prob. 11PS Ch. 5.1 - Prob. 12PS Ch. 5.1 - Prob. 13PS Ch. 5.1 - Prob. 14PS Ch. 5.1 - Prob. 15PS Ch. 5.1 - Prob. 16PS Ch. 5.1 - Prob. 17PS Ch. 5.1 - Prob. 18PS Ch. 5.1 - Prob. 19PS Ch. 5.1 - Prob. 20PS Ch. 5.1 - Prob. 21PS Ch. 5.1 - Level 1 In Problems 15-26, classify each as an...Ch. 5.1 - Prob. 23PS Ch. 5.1 - Prob. 24PS Ch. 5.1 - Prob. 25PS Ch. 5.1 - Prob. 26PS Ch. 5.1 - Prob. 27PS Ch. 5.1 - Prob. 28PS Ch. 5.1 - Prob. 29PS Ch. 5.1 - Level 1 Think of three nonassociative word triples...Ch. 5.1 - Prob. 31PS Ch. 5.1 - Prob. 32PS Ch. 5.1 - Prob. 33PS Ch. 5.1 - Prob. 34PS Ch. 5.1 - Prob. 35PS Ch. 5.1 - Prob. 36PS Ch. 5.1 - Prob. 37PS Ch. 5.1 - Prob. 38PS Ch. 5.1 - Prob. 39PS Ch. 5.1 - Prob. 40PS Ch. 5.1 - Prob. 41PS Ch. 5.1 - Prob. 42PS Ch. 5.1 - Prob. 43PS Ch. 5.1 - Prob. 44PS Ch. 5.1 - Prob. 45PS Ch. 5.1 - Prob. 46PS Ch. 5.1 - Prob. 47PS Ch. 5.1 - Prob. 48PS Ch. 5.1 - Prob. 49PS Ch. 5.1 - Prob. 50PS Ch. 5.1 - Prob. 51PS Ch. 5.1 - Prob. 52PS Ch. 5.1 - Prob. 53PS Ch. 5.1 - Prob. 54PS Ch. 5.1 - Prob. 55PS Ch. 5.1 - Problem Solving Level 3 Consider a soldier facing...Ch. 5.1 - Prob. 57PS Ch. 5.1 - Prob. 58PS Ch. 5.1 - Prob. 59PS Ch. 5.1 - Problem Solving Level 3 60. The Vanishing...Ch. 5.2 - IN YOUR OWN WORDS What is a prime number?Ch. 5.2 - Prob. 2PS Ch. 5.2 - Prob. 3PS Ch. 5.2 - Prob. 4PS Ch. 5.2 - Prob. 5PS Ch. 5.2 - Prob. 6PS Ch. 5.2 - Prob. 7PS Ch. 5.2 - Prob. 8PS Ch. 5.2 - Prob. 9PS Ch. 5.2 - Prob. 10PS Ch. 5.2 - Prob. 11PS Ch. 5.2 - Prob. 12PS Ch. 5.2 - Prob. 13PS Ch. 5.2 - Prob. 14PS Ch. 5.2 - Find all the prime numbers less than or equal to...Ch. 5.2 - Determine the largest prime you need to consider...Ch. 5.2 - Prob. 17PS Ch. 5.2 - Prob. 18PS Ch. 5.2 - Prob. 19PS Ch. 5.2 - Prob. 20PS Ch. 5.2 - Prob. 21PS Ch. 5.2 - Prob. 22PS Ch. 5.2 - Prob. 23PS Ch. 5.2 - Prob. 24PS Ch. 5.2 - Prob. 25PS Ch. 5.2 - Prob. 26PS Ch. 5.2 - Prob. 27PS Ch. 5.2 - Prob. 28PS Ch. 5.2 - Prob. 29PS Ch. 5.2 - Prob. 30PS Ch. 5.2 - Prob. 31PS Ch. 5.2 - Prob. 32PS Ch. 5.2 - Prob. 33PS Ch. 5.2 - Prob. 34PS Ch. 5.2 - Prob. 35PS Ch. 5.2 - Prob. 36PS Ch. 5.2 - Prob. 37PS Ch. 5.2 - Prob. 38PS Ch. 5.2 - Prob. 39PS Ch. 5.2 - Two movie theaters, UAI and UAII, start their...Ch. 5.2 - Prob. 41PS Ch. 5.2 - Shannon is planning a party and wants to give each...Ch. 5.2 - Boxes that are 12 inches tall are stacked next to...Ch. 5.2 - Hot dogs come in packages of 10, while buns come...Ch. 5.2 - IN YOUR OWN WORDS We used a sieve of Eratosthenes...Ch. 5.2 - Prob. 46PS Ch. 5.2 - Prob. 47PS Ch. 5.2 - Prob. 48PS Ch. 5.2 - Prob. 49PS Ch. 5.2 - Prob. 50PS Ch. 5.2 - Prob. 51PS Ch. 5.2 - Prob. 52PS Ch. 5.2 - Prob. 53PS Ch. 5.2 - Prob. 54PS Ch. 5.2 - Prob. 55PS Ch. 5.2 - What is the smallest natural number that is...Ch. 5.2 - Prob. 57PS Ch. 5.2 - Prob. 58PS Ch. 5.2 - Prob. 59PS Ch. 5.2 - Prob. 60PS Ch. 5.3 - Prob. 1PS Ch. 5.3 - Prob. 2PS Ch. 5.3 - Prob. 3PS Ch. 5.3 - Prob. 4PS Ch. 5.3 - Prob. 5PS Ch. 5.3 - Prob. 6PS Ch. 5.3 - Prob. 7PS Ch. 5.3 - Prob. 8PS Ch. 5.3 - Prob. 9PS Ch. 5.3 - Prob. 10PS Ch. 5.3 - Prob. 11PS Ch. 5.3 - Prob. 12PS Ch. 5.3 - Prob. 13PS Ch. 5.3 - Prob. 14PS Ch. 5.3 - Prob. 15PS Ch. 5.3 - Prob. 16PS Ch. 5.3 - Prob. 17PS Ch. 5.3 - Prob. 18PS Ch. 5.3 - Prob. 19PS Ch. 5.3 - Simplify the expressions in Problems 9-37. a....Ch. 5.3 - Prob. 21PS Ch. 5.3 - Prob. 22PS Ch. 5.3 - Prob. 23PS Ch. 5.3 - Prob. 24PS Ch. 5.3 - Prob. 25PS Ch. 5.3 - Prob. 26PS Ch. 5.3 - Prob. 27PS Ch. 5.3 - Prob. 28PS Ch. 5.3 - Prob. 29PS Ch. 5.3 - Prob. 30PS Ch. 5.3 - Prob. 31PS Ch. 5.3 - Prob. 32PS Ch. 5.3 - Prob. 33PS Ch. 5.3 - Prob. 34PS Ch. 5.3 - Prob. 35PS Ch. 5.3 - Prob. 36PS Ch. 5.3 - Prob. 37PS Ch. 5.3 - Prob. 38PS Ch. 5.3 - Prob. 39PS Ch. 5.3 - Prob. 40PS Ch. 5.3 - Prob. 41PS Ch. 5.3 - Prob. 42PS Ch. 5.3 - Prob. 43PS Ch. 5.3 - Prob. 44PS Ch. 5.3 - Prob. 45PS Ch. 5.3 - Prob. 46PS Ch. 5.3 - Prob. 47PS Ch. 5.3 - Prob. 48PS Ch. 5.3 - Prob. 49PS Ch. 5.3 - Prob. 50PS Ch. 5.3 - Prob. 51PS Ch. 5.3 - Prob. 52PS Ch. 5.3 - Perform the indicated operations. 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Prob. 49PS Ch. 5.4 - Prob. 50PS Ch. 5.4 - Prob. 51PS Ch. 5.4 - Prob. 52PS Ch. 5.4 - Prob. 53PS Ch. 5.4 - Prob. 54PS Ch. 5.4 - Prob. 55PS Ch. 5.4 - Prob. 56PS Ch. 5.4 - Prob. 57PS Ch. 5.4 - Prob. 58PS Ch. 5.4 - Prob. 59PS Ch. 5.4 - Prob. 60PS Ch. 5.5 - Prob. 1PS Ch. 5.5 - Prob. 2PS Ch. 5.5 - Prob. 3PS Ch. 5.5 - Prob. 4PS Ch. 5.5 - Prob. 5PS Ch. 5.5 - Prob. 6PS Ch. 5.5 - Prob. 7PS Ch. 5.5 - Prob. 8PS Ch. 5.5 - Prob. 9PS Ch. 5.5 - Prob. 10PS Ch. 5.5 - Prob. 11PS Ch. 5.5 - Prob. 12PS Ch. 5.5 - Prob. 13PS Ch. 5.5 - Prob. 14PS Ch. 5.5 - Prob. 15PS Ch. 5.5 - Prob. 16PS Ch. 5.5 - Prob. 17PS Ch. 5.5 - Prob. 18PS Ch. 5.5 - Prob. 19PS Ch. 5.5 - Prob. 20PS Ch. 5.5 - Prob. 21PS Ch. 5.5 - Prob. 22PS Ch. 5.5 - Prob. 23PS Ch. 5.5 - Prob. 24PS Ch. 5.5 - Prob. 25PS Ch. 5.5 - Prob. 26PS Ch. 5.5 - Prob. 27PS Ch. 5.5 - Prob. 28PS Ch. 5.5 - Prob. 29PS Ch. 5.5 - Prob. 30PS Ch. 5.5 - Prob. 31PS Ch. 5.5 - Prob. 32PS Ch. 5.5 - Prob. 33PS Ch. 5.5 - Prob. 34PS Ch. 5.5 - Prob. 35PS Ch. 5.5 - Prob. 36PS Ch. 5.5 - Prob. 37PS Ch. 5.5 - 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Prob. 19PS Ch. 5.6 - Prob. 20PS Ch. 5.6 - Prob. 21PS Ch. 5.6 - Prob. 22PS Ch. 5.6 - Prob. 23PS Ch. 5.6 - Prob. 24PS Ch. 5.6 - Prob. 25PS Ch. 5.6 - Carry out the operations with decimal forms in...Ch. 5.6 - Prob. 27PS Ch. 5.6 - Prob. 28PS Ch. 5.6 - Prob. 29PS Ch. 5.6 - Prob. 30PS Ch. 5.6 - Prob. 31PS Ch. 5.6 - Prob. 32PS Ch. 5.6 - Prob. 33PS Ch. 5.6 - Prob. 34PS Ch. 5.6 - Prob. 35PS Ch. 5.6 - Prob. 36PS Ch. 5.6 - Prob. 37PS Ch. 5.6 - Prob. 38PS Ch. 5.6 - Prob. 39PS Ch. 5.6 - Prob. 40PS Ch. 5.6 - Prob. 41PS Ch. 5.6 - Prob. 42PS Ch. 5.6 - Prob. 43PS Ch. 5.6 - Prob. 44PS Ch. 5.6 - Prob. 45PS Ch. 5.6 - Prob. 46PS Ch. 5.6 - Prob. 47PS Ch. 5.6 - Prob. 48PS Ch. 5.6 - Prob. 49PS Ch. 5.6 - Prob. 50PS Ch. 5.6 - Prob. 51PS Ch. 5.6 - Prob. 52PS Ch. 5.6 - Prob. 53PS Ch. 5.6 - Prob. 54PS Ch. 5.6 - Prob. 55PS Ch. 5.6 - Let be an arbitrary operation in Problems 52-59....Ch. 5.6 - Let be an arbitrary operation in Problems 52-59....Ch. 5.6 - Prob. 58PS Ch. 5.6 - Prob. 59PS Ch. 5.6 - Prob. 60PS Ch. 5.7 - 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IN YOUR OWN WORDS. What do we mean by...Ch. 5.7 - Prob. 2PS Ch. 5.7 - Prob. 3PS Ch. 5.7 - Prob. 4PS Ch. 5.7 - Prob. 5PS Ch. 5.7 - Prob. 6PS Ch. 5.7 - Level 1. Perform the indicated operations in...Ch. 5.7 - Prob. 8PS Ch. 5.7 - Prob. 9PS Ch. 5.7 - Prob. 10PS Ch. 5.7 - Prob. 11PS Ch. 5.7 - Prob. 12PS Ch. 5.7 - Prob. 13PS Ch. 5.7 - Prob. 14PS Ch. 5.7 - Prob. 15PS Ch. 5.7 - Prob. 16PS Ch. 5.7 - Prob. 17PS Ch. 5.7 - Prob. 18PS Ch. 5.7 - Prob. 19PS Ch. 5.7 - Prob. 20PS Ch. 5.7 - Prob. 21PS Ch. 5.7 - Prob. 22PS Ch. 5.7 - Prob. 23PS Ch. 5.7 - Prob. 24PS Ch. 5.7 - Prob. 25PS Ch. 5.7 - Prob. 26PS Ch. 5.7 - Prob. 27PS Ch. 5.7 - Prob. 28PS Ch. 5.7 - Prob. 29PS Ch. 5.7 - Prob. 30PS Ch. 5.7 - Prob. 31PS Ch. 5.7 - Prob. 32PS Ch. 5.7 - Prob. 33PS Ch. 5.7 - Prob. 34PS Ch. 5.7 - Prob. 35PS Ch. 5.7 - Level 2. 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If it is reduced, so state....Ch. 5.CR - Prob. 6CR Ch. 5.CR - Prob. 7CR Ch. 5.CR - Prob. 8CR Ch. 5.CR - Prob. 9CR Ch. 5.CR - Prob. 10CR Ch. 5.CR - Prob. 11CR Ch. 5.CR - Prob. 12CR Ch. 5.CR - Prob. 13CR Ch. 5.CR - Prob. 14CR Ch. 5.CR - Prob. 15CR Ch. 5.CR - Prob. 16CR Ch. 5.CR - Prob. 17CR Ch. 5.CR - Do You Weigh Too Much? In the United States, an...Ch. 5.CR - Prob. 19CR Ch. 5.CR - Prob. 20CR

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The number of roosters, hens and chicks bought by a man for $ 100 if he buys 100 birds with each rooster costing $ 10 , a hen costing $ 3 and pair of chicks costing $ 1 and he buys at least one of each type.

Solution Summary: The author explains the method of solving the system of equations by substitution method through the following steps.

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To find:

The number of roosters, hens and chicks bought by a man for $100 if he buys 100 birds with each rooster costing $10, a hen costing $3 and pair of chicks costing $1 and he buys at least one of each type.

Want to see the full answer?

Chapter 5 Solutions

The number of roosters, hens and chicks bought by a man for $ 100 if he buys 100 birds with each rooster costing $ 10 , a hen costing $ 3 and pair of chicks costing $ 1 and he buys at least one of each type.

Solution Summary: The author explains the method of solving the system of equations by substitution method through the following steps.

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To find: The number of roosters, hens and chicks bought by a man for $100 if he buys 100 birds with each rooster costing $10, a hen costing $3 and pair of chicks costing $1 and he buys at least one of each type.

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Chapter 5 Solutions

To find:

The number of roosters, hens and chicks bought by a man for $100 if he buys 100 birds with each rooster costing $10, a hen costing $3 and pair of chicks costing $1 and he buys at least one of each type.