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A room measures 6m long and 4m wide. A carpet whose area is #15m^2# is laid in the middle of the room leaving a margin of uniform width all-round the room.
a) Taking x m to represent the width of the margin, express the dimensions of the carpet in terms of x.
b) Write down a simplified expression for the area of the carpet in terms of x.
c) Find two possible values of x and hence state the actual width of the margin.
d) Calculate the cost of covering the margin with a material which costs sh 250 per square metre.