Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.3 Applications of Linear Equations - Exercise Set 6.3 - Page 376: 71



Work Step by Step

It is given that on each correct answer I have paid 8c and on each wrong answer fine is 5c. Let as suppose that I have done \[X\] problems correctly and have done \[Y\]problems wrong So, total question I have done \[X+Y=26\]……(1) And the money exchanged between us is zero, we can write it in algebraic expression \[8X-5Y=0\] \[8X=5Y\]…… (2) Rewrite equation (1)as follows: \[X=26-Y\] Now, substitute this value in the equation (2) and solve for Y. \[\begin{align} & 8\left( 26-Y \right)=5Y \\ & 208-8Y=5Y \\ & -13Y=208 \\ & Y=16 \end{align}\] Now when substitute back the value of Y in equation (1)to obtain, \[\begin{align} & X=26-16 \\ & X=10 \\ \end{align}\] Where X is the number of Questions I have done correctly. 10 problems were solved correctly.
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