Forming Equations
Before solving an equation you may need to form it from the information given in the question.
How do I form an expression?
- An expression is an algebraic statement without an equals sign e.g. or
- Sometimes we need to form expressions to help us express unknown values
- If a value is unknown you can represent it by a letter such as
- You can turn common phrases into expressions
- Here you can represent the "something" by any letter
2 less than "something" Double the amount of "something" 5 lots of "something" 3 more than "something" Half the amount of "something"
- Here you can represent the "something" by any letter
- You might need to use brackets to show the correct order
- "something" add 1 then multiplied by 3
- which simplifies to
- "something" multiplied by 3 then add 1
- which simplifies to
- "something" add 1 then multiplied by 3
- To make the expression as easy as possible choose the smallest value to be represented by a letter
- If Adam is 10 years younger than Barry, then Barry is 10 years older than Adam
- Represent Adam's age as then Barry's age is
- This makes the algebra easier, rather than calling Barry's age and Adam's age
- 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 Adams's age
- If Adam is 10 years younger than Barry, then Barry is 10 years older than Adam
How do I form an equation?
- An equation is simply an expression with an equals sign that can then be solved
- You will first need to form an expression and make it equal to a value or another expression
- It is useful to know alternative words for basic operations:
- For addition: sum, total, more than, increase, etc
- For subtraction: difference, less than, decrease, etc
- For multiplication: product, lots of, times as many, double, triple etc
- For division: shared, split, grouped, halved, quartered etc
- Using the first example above
- If Adam is 10 years younger than Barry and the sum of their ages is 25, you can find out how old each one is
- Represent Adam's age as then Barry's age is
- We can solve the equation or
- If Adam is 10 years younger than Barry and the sum of their ages is 25, you can find out how old each one is
- Sometimes you might have two unrelated unknown values (x and y) and have to use the given information to form two simultaneous equations
Worked example
At a theatre the price of a child's ticket is and the price of an adult's ticket is .
Write equations to represent the following statements: