Forming Equations from Words (Cambridge (CIE) IGCSE International Maths)

Forming Linear Equations

How do I form expressions from words?

• You can turn common phrases into expressions

  • Use x to represent an unknown value

    2 less than "something"
    Double "something"
    5 lots of "something"
    3 more than "something"
    Half of "something"

• Common words indicating basic operations are:

  • Addition: sum, total, more than, increase

  • Subtraction: difference, less than, decrease

  • Multiplication: product, lots of, times as many, double, triple

  • Division: shared, split, grouped, halved, quartered

• Brackets help keep the order correct

  • "something" add 1, then multiplied by 3

    • which simplifies to 

  • Compare this to "something" multiplied by 3, then add 1

    • which simplifies to 

• You may have to choose which unknown to call x

  • If Adam is 10 years younger than Barry, then Barry is 10 years older than Adam

    • Either represent Adam's age as and Barry's age as

    • Or represent Adam's age as and Barry's age as

  • If Adam's age is half of Barry's age, then Barry's age is double Adam's age

    • So if Adam's age is then Barry's age is

    • This makes the algebra easier (rather than using for Barry's age and for Adam's age)

How do I form equations?

• An equation is a statement with an equals sign that can be solved

• Try to put in the phrase "is equal to" to see where the equals goes

  • Lisa's age is double Aisha's age and the sum of their ages is ("is equal to") 27 

    • Represent Aisha's age as and Lisa's age is

    • The equation is 

  • When solving, always give the answer in context

    • so 

    • In context: "Lisa is 18 years old and Aisha is 9 years old"

• Sometimes you might have two unknown values (x  and y)

  • Use the information to form two simultaneous equations