Forming and solving equations

Three steps

1. Say what x stands for ("let a child ticket cost £x").
2. Write an equation from the facts: totals, perimeters, angle sums (180° on a line or in a triangle, 360° round a point).
3. Solve, then answer the question asked: often a length, an angle or a price, not x itself.

1. an adult ticket is £4 more than a child ticket; 2 adults and 3 children pay £43
2. 2(x + 4) + 3x = 43
3. 5x + 8 = 43
4. x = 7: a child ticket costs £7

More ways to name the unknown:

• Ages: Sam is x, his aunt is 12 years older, so x + 12. Ages add to 50: x + x + 12 = 50, so x = 19.
• Consecutive whole numbers follow each other: n, n + 1, n + 2. Three of them add to 48: 3n + 3 = 48, so n = 15, the smallest.
• An isosceles triangle has two equal sides (and two equal angles). Sides (2x + 1), (2x + 1) and (x + 3) with perimeter 24: 5x + 5 = 24, so x = 3.8.
• A rectangle's perimeter is 2 × length + 2 × width.
• "I think of a number": treble it and subtract 4, which is the same as doubling it and adding 9. 3n − 4 = 2n + 9, so n = 13.
• After finding x, substitute it back if the question asks for an angle or a length: angles x°, 2x° and (x + 20)° in a triangle give 4x + 20 = 180, so x = 40 and the largest angle is 80°.