Forming & Solving 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"
- Use x to represent an unknown value
- 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
- "something" add 1, then multiplied by 3
- 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)
- If Adam is 10 years younger than Barry, then Barry is 10 years older than Adam
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"
- Lisa's age is double Aisha's age and the sum of their ages is ("is equal to") 27
- Sometimes you might have two unknown values (x and y)
- Use the information to form two simultaneous equations
Worked example
A flowerbed has flowers of three different colours: red, yellow and purple.
The number of yellow flowers is three times the number of red flowers.
The number of purple flowers is 5 more than the number of yellow flowers.
If the difference between the number of purple flowers and red flowers is 29, find the number of yellow flowers.
Let the number of red flowers be x
red flowers
Multiply this by 3 to get the number of yellow flowers
yellow flowers
Add 5 to the previous result to get the number of purple flowers
purple flowers
Find the difference between the number of purple and red flowers (purple subtract red, as purple is larger)
Set the difference equal to 29
Simplify the left-hand side (3x - x = 2x)
Solve the equation (subtract 5 then divide by 2)
This is not the answer to the question asked
The number of yellow flowers is 3x so multiply this answer by 3
There are 36 yellow flowers