This part is the most challenging yet. It requires a degree of conceptual thought. Practise as always will carve this skill groove deeper within your mind, but be prepared to get things incorrect in this section.

\begin{examplebox}
    \begin{questions}
        \Question[1] Find a formula for \(n\), the number of cents in \(x\) dollars and \(y\) cents.
        \begin{solutionordottedlines}[2cm]
            In \(\$ x\) there are \(100 x\) cents.

            In \(\$ x\) and \(y\) cents there are \((100 x+y)\) cents.

            The formula is \(n=100 x+y\).
        \end{solutionordottedlines}
        \Question[2] Here is an isosceles triangle with equal base angles marked. Find a formula for \(\beta\) in terms of \(\alpha\).
        \begin{tikzpicture}
        \end{tikzpicture}
        \begin{solutionordottedlines}[2cm]
            \[
            \begin{aligned}
            \alpha+2 \beta & =180 \quad \text { (angle sum of triangle) } \\
            2 \beta & =180-\alpha \\
            \beta & =\frac{180-\alpha}{2}
            \end{aligned}
            \]
        \end{solutionordottedlines}
        \Question[4] Construct a formula for:
         \begin{parts}                                                                                      
             \part \(D\) in terms of \(n\), where \(D\) is the number of degrees in \(n\) right angles      
             \begin{solutionordottedlines}[1cm]                                                             
                 \(D = 90n\)                                                                                
             \end{solutionordottedlines}                                                                    
             \part \(c\) in terms of \(D\), where \(c\) is the number of cents in \(\$ D\)                  
             \begin{solutionordottedlines}[1cm]                                                             
                 \(c = 100D\)                                                                               
             \end{solutionordottedlines}                                                                    
             \part \(m\) in terms of \(h\), where \(m\) is the number of minutes in \(h\) hours             
             \begin{solutionordottedlines}[1cm]                                                             
                 \(m = 60h\)                                                                                
             \end{solutionordottedlines}                                                                    
             \part \(d\) in terms of \(m\), where \(d\) is the number of days in \(m\) weeks                
             \begin{solutionordottedlines}[1cm]                                                             
                 \(d = 7m\)                                                                                 
             \end{solutionordottedlines}                                                                    
         \end{parts}                                                                                        
    \end{questions}
\end{examplebox}

 \begin{exercisebox}                                                                                        
     \begin{questions}                                                                                      
         \Question[4] Construct a formula for:                                                              
         \begin{parts}                                                                                      
             \part the number of centimetres \(n\) in \(p\) metres                                          
             \begin{solutionordottedlines}[1cm]                                                             
                 \(n = 100p\)                                                                               
             \end{solutionordottedlines}                                                                    
             \part the number of millilitres \(s\) in \(t\) litres                                          
             \begin{solutionordottedlines}[1cm]                                                             
                 \(s = 1000t\)                                                                              
             \end{solutionordottedlines}                                                                    
             \part the number of centimetres \(q\) in \(5 p\) metres                                        
             \begin{solutionordottedlines}[1cm]                                                             
                 \(q = 500p\)                                                                               
             \end{solutionordottedlines}                                                                    
             \part the number of grams \(x\) in \(\frac{y}{2}\) kilograms                                   
             \begin{solutionordottedlines}[1cm]                                                             
                 \(x = 500y\)                                                                               
             \end{solutionordottedlines}                                                                    
         \end{parts}                                                                                        
         \Question[6] Find a formula relating \(x\) and \(y\) for each of these statements, making \(y\) th 
 subject.                                                                                                   
         \begin{parts}                                                                                      
             \part \(y\) is three less than \(x\).                                                          
             \begin{solutionordottedlines}[1cm]                                                             
                 \(y = x - 3\)                                                                              
             \end{solutionordottedlines}                                                                    
             \part \(y\) is four more than the square of \(x\).                                             
             \begin{solutionordottedlines}[1cm]                                                             
                 \(y = x^2 + 4\)                                                                            
             \end{solutionordottedlines}                                                                    
             \part \(y\) is eight times the square root of one-fifth of \(x\).                              
             \begin{solutionordottedlines}[1cm]                                                             
                 \(y = 8 \sqrt{\frac{x}{5}}\)                                                               
             \end{solutionordottedlines}                                                                    
             \part \(x\) and \(y\) are supplementary angles.                                                
             \begin{solutionordottedlines}[1cm]                                                             
                 \(y = 180 - x\)                                                                            
             \end{solutionordottedlines}                                                                    
             \part A car travelled \(80 \mathrm{~km}\) in \(x\) hours at an average speed of \(y \mathrm{~k} / \mathrm{h}\).                                                                                            
             \begin{solutionordottedlines}[1cm]                                                             
                 \(y = \frac{80}{x}\)                                                                       
             \end{solutionordottedlines}                                                                    
             \part A car used \(x\) litres of petrol on a trip of \(80 \mathrm{~km}\) and the fuel          
 consumption was \(y\) litres \(/ 100 \mathrm{~km}\).                                                       
             \begin{solutionordottedlines}[1cm]                                                             
                 \(y = \frac{x}{80} \times 100\)                                                            
             \end{solutionordottedlines}                                                                    
         \end{parts}                                                                                        
         \Question[6] Find a formula relating the given pronumerals for each of these statements.           
         \begin{parts}                                                                                      
             \part The number of square \(\mathrm{cm} x\) in \(y\) square metres                            
             \begin{solutionordottedlines}[1cm]                                                             
                 \(x = 10000y\)                                                                             
             \end{solutionordottedlines}                                                                    
             \part The selling price \(\$ S\) of an article with an original price of \(\$ m\) when a       
 discount of \(20 \%\) is given                                                                             
             \begin{solutionordottedlines}[1cm]                                                             
                 \(S = m - 0.2m\)                                                                           
             \end{solutionordottedlines}                                                                    
             \part The length \(c \mathrm{~cm}\) of the hypotenuse and the lengths \(a \mathrm{~cm}\) and \( \mathrm{~cm}\) of the other two sides in a right-angled triangle                                           
             \begin{solutionordottedlines}[1cm]                                                             
                 \(c = \sqrt{a^2 + b^2}\)                                                                   
             \end{solutionordottedlines}                                                                    
             \part The area \(A \mathrm{~cm}^{2}\) of a sector of a circle with a radius of length \(r = \mathrm{~cm}\) and angle \(\theta\) at the centre of the circle                                            
             \begin{solutionordottedlines}[1cm]                                                             
                 \(A = \frac{1}{2} r^2 \theta\)                                                             
             \end{solutionordottedlines}                                                                    
             \part The distance \(d \mathrm{~km}\) travelled by a car in \(t\) hours at an average speed of \(75 \mathrm{~km} / \mathrm{h}\)                                                                           
             \begin{solutionordottedlines}[1cm]                                                             
                 \(d = 75t\)                                                                                
             \end{solutionordottedlines}                                                                    
             \part The number of hectares \(h\) in a rectangular paddock of length \(400 \mathrm{~m}\) and width \(w \mathrm{~m}\)                                                                                    
             \begin{solutionordottedlines}[1cm]                                                             
                 \(h = \frac{400w}{10000}\)                                                                 
             \end{solutionordottedlines}                                                                    
         \end{parts}                                                                                        
     \end{questions}                                                                                        
 \end{exercisebox}                                                                                          
