## Thinking Mathematically (6th Edition)

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.