Painting a track inside a rectangular field

A school field is a rectangle measuring \((2x+7)\) m by \((2x+3)\) m, where \(x>0\). A track of uniform width \(1\) m is painted along the inside of the boundary of the field.

1. Show that the area of the track is \((8x+16)\text{ m}^2\).[3]
2. Paint costs \(\$2.40\) per square metre and the budget is \(\$300\). Find the greatest whole-number value of \(x\) for which the track can be painted within budget, and state one assumption you have made.[3]
3. A student says that doubling \(x\) doubles the area of the track. Use (a) to show that the student is wrong, and state which part of the track area does double.[2]