Formulae Tool and Car Hire

1
Wednesday, 30 September 2009
Formulae Tool and Car Hire
Why am I doing this?

• You will probably want to hire a tool or tools
  for DIY project or a car or clothes for some
  special occasion. Its good to understand the
  hire charge.
• You might want to start your own tool/car/clothes
  hire business.
• These questions are real favourites with the SAT
  and GCSE examiners.

2
Understanding the Idea Level 5 - 6
It is important to understand the idea of how
payment is made for hiring. After viewing the
this section, you should be able to say,
I get it!
3
How much will you pay for
Top hat and tails at 20 plus 5 per day for 3
days?
Cost 20 5 X 3 35
A wedding car at 150 plus 20 per hour for 5
hours?
Cost 150 20 X 5 250
A concrete mixer at 40 plus 10 per day for 7
days?
Cost 40 10 X 7 110
A car at 150 plus 10p per mile? You travel 150
miles in this car.
Cost 150 150 X 10 100 165
4

• Level 5 - 6 success if you can calculate
• The charge for hiring a breaker drill is 20 and
  then 5 per day. What will be the cost if I hire
  it for 3 days?
• The charge for hiring a car at 60 plus 20 per
  day for 2 days.
• The hire charge for a concrete mixer is 25 plus
  15 per day. What will I be charged for 4 days?
• The cost of hiring a boat at 100 plus 25 per
  day for 4 days.

5

• Level 5 - 6 success if you can calculate
• Cost 20 5 X 3
• 20 15 35
• 2. Cost 60 20 X 2
• 60 40 100
• 3. Cost 25 15 X 4
• 25 60 85
• 4. Cost 100 25 X 4
• 100 100 200

6
Writing a Formula (Rule) to Find the Cost of
Hiring Level 6 - 7
After working through this section, you should be
able to write a formula for the cost of hiring.
7
Write a formula (rule) for hiring a car when it
costs 40 and then 10 per day. Make the letter c
cost and d days for this problem.
Cost 40 10 x number of days
The cost (10) per day
The amount that you have to pay no matter how
long you hire the car
8
Write a formula (rule) for hiring a car when it
costs 40 and then 10 per day. Make the letter c
cost and d days for this problem.
Cost 40 10 x number of days C 40 10 x
d
The letter d stands for the number of days
We dont need to write the times sign
The letter C stands for the COST
C 40 10d
9
Amy has started a tool hire business. She charges
50 plus 10 per day for a concrete mixer. a) If
you hire the mixer for 3 days, what will be the
hire charge? b) Write a formula for the cost (C)
and in terms of the days (d)

• Cost 50 10 x 3 ? Cost 50 30
• 80

Always Pay
Number days
Charge per day
b) C 50 10 x d C 50 10d
No need to write the times sign
10

• Level 6 - 7 success if you can write formulae for
• The charge for hiring a breaker drill is 20 and
  then 5 per day. a) What will be the cost if I
  hire it for 3 days? b) Write a formula for the
  cost C in terms of the time d.
• A car hire firm charges 50 plus 30 per day.
  Write this as a formula with C Cost and d
  days.
• The cost of hiring a carpet cleaner is 10 plus
  2 per hour. Write a formula for the cost C in
  terms of the time h.
• The cost of hiring a mini digger is 120 plus 10
  per hour. Write a formula for the hire charge C
  in terms of the time t.

11

• Answers - Level 6 - 7 success?
• a) Cost 20 5 x 3 Ans. 35
• b) C 20 5d
• C 50 30d
• C 10 2h
• C 120 10t

12
Altering the Subject of the Formula Level 7 8

After working through this section, you should be
able to change the subject of the formula from C
to d
13
The hire charge for a car is 40 plus 20 per day
is given by the formula C 40 20d Make d the
subject of this formula.
Take 40 from both side
C 40 20d C 40 40 20d 40 C 40
20d 20d C 40 d (C 40) 20
Write with 20d at the front
Divide by 20
14

• Level 7 8 Success if you can
• Make d the subject of this formula
• C 10 2d
• 2. Make t the subject of this formula
• C 20 5t
• 3. Make d the subject of this formula
• C 40 10d
• 4. Make m the subject of this formula
• C 100 20m
• 5. Make t the subject of this formula
• C 120 6t

15

• Level 7 8 Success if you can
• Make d the subject of this formula
• C 10 2d d (C 10) 2
• 2. Make t the subject of this formula
• C 20 5t t (C 20) 5
• 3. Make d the subject of this formula
• C 40 10d d (C 40) 10
• 4. Make m the subject of this formula
• C 100 20m m (C 100) 20
• 5. Make t the subject of this formula
• C 120 6t t (C 120) 6

16

• Level 7 8 Success
• 2. The hire charge for a car is 40 plus 20 per
  day. If I am charged 100, for how many days did
  I hire the car?
• 3. The hire charge for a carpet cleaner is 20
  plus 10 per day. If I am charged 70, for how
  many days did I hire the cleaner?
• 4. I am charged 120 for the hire of a concrete
  mixer. If the hire charge is 60 plus 20 per
  day, for how many days did I hire the mixer?
• 5. For how many days will a person have hired a
  mini digger if the cost is 250 and the hire
  charge is 125 plus 25 per day?

17
Level 7 Success 1. 3 days 2. 5 days 3. 3
days 4. 5 days
18
Formulae Tool and Car Hire

• Success if
• The charge for hiring a breaker drill is 20 and
  then 5 per day. What will be the cost if I hire
  it for 3 days?
• A car hire firm charges 50 plus 30 per day.
  Write this as a formula with C Cost and d
  days.
• A formula for hiring a van is
• C 100 20d
• Write a formula for days (d) when you know the
  cost (C).
• If the charge is 180, for how many days has the
  van been hired?

5 - 6
6 - 7
7 - 8
19

• 35
• C 50 30d
• d (C 100) 20
• 4 days