5. (a) Aisha is designing a rectangular garden that measures 15 m by 19·5 m. It has a fence around the outside and the following features:


● A patio at the front of the garden, 15 m × 4·5 m rectangle A lawn, 15 m × 12 m rectangle


●


● A path between lawn and vegetable patch, 15 m × 1·5 m rectangle ●


A vegetable patch at the back of the garden, next to the fence, 15 m by 1·5 m rectangle


Draw a plan of Aisha’s garden using the scale 1 m = 1 cm.


(b) Aisha has the following two choices of paving stone for the 15 m by 4·5 m patio: Size Each pack covers Cost per pack


Stones A Stones B


8·6 m2 7·4 m2


€139·75 €128·50


Given that she can only buy full packs of stones, which stones should Aisha choose to get the lowest price? Justify your answer.


(c) (i) Calculate the area of the garden taken up by the vegetable patch and the lawn.


(ii) Express the answer to (i) as a percentage of the total area of the garden. Give your answer correct to two signifi cant fi gures.


6. (a) Bob is a painter. He wants to mix white and black paint to make grey paint. He uses 6 litres of white paint and 4 litres of black paint to make 10 litres of grey paint.


(i) What is the ratio (in simplest form) of white to black paint in the grey paint? (ii) How much black paint would he need to make 25 litres of grey paint?


(b) Bob needs to paint three rectangular walls using this grey colour. The dimensions of these walls are: • Wall A: width 4·5 m and length 3·1 m • Wall B: width 5·2 m and length 2·8 m • Wall C: width 4·9 m and length 3·2 m If 1 litre of the grey mix covers 16 m2


(i) and he is going to paint 2 coats on each wall, how much paint will he need to paint the three walls? Give your answer to the nearest litre.


(ii) How much white and black paint will he need to make enough grey to paint the three walls? (c) Bob charges a €100 fl at fee plus €50 an hour for his painting service.


(i) Identify the variables and the constants in this situation. Explain the meaning of any letters you have used.


(ii) Form an equation to represent the cost of a painting job done by Bob, for any number of hours. (iii) Copy and complete the following table:


Time (hours) Cost (€)


0 100


(iv) Draw a graph to represent the cost of a 10-hour job. (v) Find the slope of the graph.


(vi) Use your graph to estimate the cost of a 5·5-hour job and verify your answer using the equation you formed in part (ii).


(vii) Use your graph to estimate how long Bob was working if he earned €275. Verify your answer using the equation you formed in part (ii).


1 2 3 4 5 6 7 8


Make a rough sketch fi rst, before you try to draw the garden to scale. This will help you to visualise what the garden looks like.


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Linking Thinking 1


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