Formulae – Tool and Car Hire

Friday, April 21, 2023

•You will probably want to hire a tool or tools for DIY project or a car or clothes for some special occasion. It’s 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.

Why are we doing

this?

Understanding the Idea

Level 5 - 6

I get it!

How much will you pay if

You hire a top hat and tails for 3 days at £20 plus £5 per day?

You hire a wedding car for 5 hours at £150 plus £20 per hour?

You hire a concrete mixer for 7 days at £40 plus £10 per day?

A car at £150 plus 10p per mile? You travel 150 miles in this car.

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

Level 5 - 6 success if you can calculate

1. 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?

2. The charge for hiring a car at £60 plus £20 per day for 2 days.

3. The hire charge for a concrete mixer is £25 plus £15 per day. What will I be charged for 4 days?

4. The cost of hiring a boat at £100 plus £25 per day for 4 days.

Level 5 - 6 success if you can calculate

1. 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

Writing a Formula (Rule) to Find the Cost

Level 6 - 7

Cost =(Rule) C =

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 amount that you have to pay no matter how

long you hire the car

The cost (£10) per day

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

The letter C stands for the

COST

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

C = 40 + 10d

We don’t need to write

the times sign

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)

a) Cost = 50 +

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)

a) Cost = 50 + 10 x 3

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)

a)Cost = 50 + 10 x 3

= 50 + 30 Ans. £80

Amy has started a tool hire business. She charges £50 plus £10 per day for a concrete mixer.

If you hire the mixer for 3 days, what will be the hire charge?

Write a formula for the cost (C) and in terms of the days (d)

a)Cost = 50 + 10 x 3

= 50 + 30 Ans. £80

b) C = 50 + 10 x d

Amy has started a tool hire business. She charges £40 plus £10 per day for a concrete mixer.

If you hire the mixer for 3 days, what will be the hire charge?

Write a formula for the cost (C) and in terms of the days (d)

a)Cost = 50 + 10 x 3

= 50 + 30 Ans. £80

b) C = 50 + 10 x d

C = 50 + 10d

Level 6 - 7 success if you can write formulae for

1. 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.

2. A car hire firm charges £50 plus £30 per day. Write this as a formula with C = Cost and d = days.

3. 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.

4. 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.

Answers - Level 6 - 7 success?

1.a) Cost = 20 + 5 x 3 Ans. £35

b) C = 20 + 5d

2. C = 50 + 30d

3. C = 10 + 2h

4. C = 120 + 10t

Altering the Subject of the FormulaLevel 7 – 8

C = 40 + 20d d =

40 and C and 20

You want d at the

front

TheSUBJECT

The hire charge for a car is £40 plus £20 per day is given by the formula below. Make d the subject of this formula.

C = 40 + 20d

The hire charge for a car is £40 plus £20 per day is given by the formula below. Make d the subject of this formula.

C = 40 + 20d

C – 40 = 20d

Take 40 from both

side

The hire charge for a car is £40 plus £20 per day is given by the formula below. Make d the subject of this formula.

C = 40 + 20d

C – 40 = 20d

20d = (C – 40)

Write with 20d at the

front

The hire charge for a car is £40 plus £20 per day is given by the formula below. Make d the subject of this formula.

C = 40 + 20d

C – 40 = 20d

20d = (C – 40)

d = (C – 40) ÷ 20 Divide by 20

Level 7 – 8 Success if you can…

1. 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 +

10d4. Make m the subject of this formula :

C = 100 + 20m5. Make t the subject of this formula :

C = 120 + 6t

Level 7 – 8 Success if you can…

1. 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

Level 7 – 8 Success

1. 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?

Level 7 Success

1. 3 days

2. 5 days

3. 3 days

4. 5 days

Formulae – Tool and Car Hire

Success if…

1. 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?

2. A car hire firm charges £50 plus £30 per day. Write this as a formula with C = Cost and d = days.

3. 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

1) £35

2) C = 50 + 30d

3) d = (C – 100) ÷ 20

4 days