Problems where you set up the algebra yourself: sides and angles in x, ages and tickets, areas that give a quadratic, sequences and inequalities.
What you will learn
- Choose a letter for the unknown and write each quantity with it
- Form an equation or inequality from the words
- Solve it and use the solution to answer the question asked
- Reject a solution that makes no sense
From words to an equation
- say what x is: "let Ben be x years old"
- write every quantity with x: Amira is x + 5, Chloe is 2x
- use the fact you are given: x + 5 + x + 2x = 41
- solve: 4x + 5 = 41, so 4x = 36 and x = 9
- answer the question asked: Amira is 9 + 5 = 14
The usual slip: stopping at x. The question asked for Amira's age, or the area, or the largest angle, so finish the job.
The fact you are given can be a total of angles (180° in a triangle, 360° in a quadrilateral) or a perimeter. A rectangle (3x − 1) by (x + 2) with perimeter 34: 2(3x − 1) + 2(x + 2) = 8x + 2 = 34, so x = 4. It is 11 by 6, with area 66.
The rest of this lesson and its 12 practice questions are locked.
In this lesson
- From words to an equation
- Two unknowns: simultaneous equations
- When the algebra gives two answers
- Inequalities and sequences
- Try it: An easy one first
12 practice questions, marked as you go; about 30 minutes in all.
Key terms
Whole number
In this unit: Putting it together
Multi-step problems in real contexts, where one result feeds the next: number, algebra, ratio, geometry and statistics, Foundation and Higher, with and without a calculator, checked step by step.