3. Dustin is baking a Christmas cake. He has a choice of two ovens. A normal oven, or a fan assisted oven. The time it takes to bake the Christmas cake in each oven is given by the following formulae:


Normal oven: t = 7·5w + 40 Fan oven:


t = 3·25w + 30


where w = mass in kilograms and t = time taken in minutes.


(i) How much quicker is it to cook a small 4 kilogram Christmas cake in a fan oven than in a normal oven?


(ii) How much slower would it be to cook a 6 kilogram Christmas cake in a normal oven than in a fan oven?


(iii) How many kilograms is the Christmas cake if it takes 4 hours and 55 minutes to fully cook in a normal oven?


4. Mike’s grandfather is six times the present age of Mike. After 5 years, their ages will add to 87. Find their present ages.


5. (a)


Complete the pattern in each of the mapping diagrams provided, and create a rule for each.


(b) Are all patterns linear? Justify your answer, showing all work.


(i)


1 3


4 2


5 6


Input Output (ii)


1 3


4 2


5 6


Input Output


4 8


12


1 4 9


(iii)


1 3


4 2


5 6


Input Output


2 8


14


6. Emma’s courier service has a unique pricing structure. She charges €4·10 to pick up your parcel, and then a fi xed charge of €1·03 per km she must travel to deliver your package.


(i) Write an expression to show how much Emma will charge for any distance travelled.


(ii) Umer wants a package collected and delivered to a location 5 km away. How much will it cost him?


(iii) Bruno has €20. He wants to have a package picked up and delivered to a location 17·5 km away. Does he have enough money? Justify your answer with supporting work.


(iv) Draw a graph showing how much money it would cost to pick up a parcel and deliver it to a location up to and including 15 km away.


(v) Is your graph linear? Justify your answer.


(vi) How much would it cost to have a parcel picked up and delivered a distance of 4·5 km? Use your graph from part (iv) or any other valid mathematical method to answer.


(vii) Emma wants to change her pricing policy, so that it now costs


c = 0·5 + 1·5d


where c = total cost and d = distance travelled.


Discuss, using any valid mathematical method, which pricing structure is better. Justify your answer.


Now that you have completed the unit, revisit the


Something to think about …


question posed at the start of this unit. 159


9 Solving linear relations


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