A plumber has a call out fee of £40, plus
an hourly rate of £18. Write a formula to
calculate the cost of any job and calculate
the cost of a job estimated to take 2
hours.
A job to take 2 hours would look
like T= 40+18h x 2 (40+36) = £76
BIDMAS is used to do the
multiplication before addition
The total cost (which would be
symbolised as 'T') would be equal
to the call out charge
Plus the £18 for the hourly charge
(would be symbolised as 'h')
SECOND EXAMPLE
On a given day the plumber
charges £130. How long did the
plumber work for?
Total cost doesn't need
calculating - the hours do
FORMULAE = T= 40+18h
130= 40 + 18h
FIRST - Take 40 from both sides (130 AND 40)
90 = 18h
SECOND - Divide both sides by 18
5 = h
NUMBER OF HOURS WORKED = 5
Changing Subject of a Formula
The subject of a formula is the variable that is being
worked out. It can be recognised as the letter on its
own on one side of the equation.
For example, in the formula for the
area of a rectangle Equation: A = bh
(Equation: text{area} = text{base}
times text{height}), the subject of
the formula is Equation: A.
The subject is the
thing that is being
worked out
If the area and height of a rectangle
was known and the base of the
rectangle was required instead, the
formula Equation: A = bh wouldn't help
as it is Equation: b that now needs to be
calculated.
A = bh means A = b times h. To make b
the subject of the formula,b needs to be
isolated. In the formula above, the letter b
is multiplied by h. The inverse of
multiplying by h is dividing by h, so divide
both sides by h to isolate b.
EXAMPLE
Rearrange the formula v = u + at to make u
the subject of the formula.
Answer this
question by
finding the letter
Equation: u in
the formula.
Isolate this letter by inversing any other items on
this side of the equation. Next to the u, there is
also a + at. The inverse of adding at is subtracting
at, so subtract at from both sides.