Explanation Given Information: Hal gave Tom as many raffle tickets as Tom first had and Gary as many as Gary first had. Tom gave Hal and Gary as each then has. Gary gave Hal and Tom as many tickets as each then had. Each of them, finally, have 40 tickets. Formula used: To solve a system of linear equations with 3 unknowns, 1) Familiarize the variables. 2) Translate the given statements into numeric form. 3) Perform calculations to find the values of the 3 unknowns. 4) Check the solution. The distributive property of multiplication states that for real numbers a , b and c , a ⋅ ( b + c ) = a ⋅ b + a ⋅ c Calculation: Consider the number of tickets with Tom to be x , the number of tickets with Gary to be y and the number of tickets with Hal to be z . Hal gave Tom as many raffle tickets as Tom first had and Gary as many as Gary first had. The tickets with Tom become 2 x , the tickets with Gary become 2 y and the tickets with Hal become z − x − y . Tom gave Hal and Gary as each then has. The tickets with Gary are 2 y + 2 y = 4 y The tickets with Hal are z − x − y + z − x − y = 2 ( z − x − y ) And, the tickets with Tom are 2 x − 2 y − ( z − x − y ) = 2 x − 2 y − z + x + y = 3 x − y − z Gary gave Hal and Tom as many tickets as each then had. The tickets with Hal are 2 ( z − x − y ) + 2 ( z − x − y ) = 4 ( z − x − y ) = − 4 x − 4 y + 4 z The tickets with Tom are 3 x − y − z + 3 x − y − z = 2 ( 3 x − y − z ) = 6 x − 2 y − 2 z And, the tickets with Gary are 4 y − 2 ( z − x − y ) − ( 3 x − y − z ) = 4 y − 2 z + 2 x + 2 y − 3 x + y + z = − x + 7 y − z Each of them, finally, has 40 tickets. Thus, the final tickets with Hal, Tom and Gary are equal to 40

6th Edition

ISBN: 9780321848741

Author: Marvin L. Bittinger

Publisher: PEARSON

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Chapter 8.5, Problem 43ES

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To calculate: The number of tickets Tom had in the beginning if each has 40 tickets in the end.

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Chapter 8.5, Problem 42ES

Chapter 8.5, Problem 44ES

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Chapter 8 Solutions

Elementary and Intermediate Algebra

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The number of tickets Tom had in the beginning if each has 40 tickets in the end.

Solution Summary: The author explains the formula used to solve a system of linear equations with 3 unknowns.

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