These are the Paper 2 questions where nobody hands you the equation — you build it. The method is always the same three moves. Choose the quantity you know least about and call it a letter. Write every other quantity in terms of that letter. Then find the sentence that says two things are equal — a total, a perimeter, an amount left over — and turn it into an equation. Solve it, and read the question again to check which number it actually asked for: the letter is often not the final answer.
Worked example
Problem The perimeter of a rectangular garden is 44 m. The length is y m and the breadth is 8 m shorter than the length. Find the length, then the area.
The breadth is 8 less than the length, so in terms of y it is y − 8 metres.
Perimeter is two lengths and two breadths: y + (y − 8) + y + (y − 8) = 44, which collects to 4y − 16 = 44.
Add 16 to both sides: 4y = 44 + 16 = 60, so y = 60 ÷ 4 and the length is 15 m.
The breadth is 15 − 8 = 7 m, so the area is 15 × 7 = 105 m².
Watch out The breadth appears TWICE in a perimeter, so the 8 is taken off twice — that is where the 16 comes from, not 8.
