1. Formulae – Tool and Car Hire Friday, 18 September 2015 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?

2. Understanding the Idea Level 5 - 6 I get it!

3. 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.

4. 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

5. 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.

6. 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

7. Writing a Formula (Rule) to Find the Cost Level 6 - 7 Cost =(Rule) C =

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 The amount that you have to pay no matter how long you hire the car The cost (£10) per day

9. 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

10. 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

11. 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 +

12. 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

13. 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

14. 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

15. 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

16. 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.

17. 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

18. Altering the Subject of the Formula Level 7 – 8 C = 40 + 20d d = 40 and C and 20 You want d at the front The SUBJECT

19. 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

20. 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

21. 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

22. 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

23. 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 + 10d 4. Make m the subject of this formula : C = 100 + 20m 5. Make t the subject of this formula : C = 120 + 6t

24. Level 7 – 8 Success if you can… 1.Make d the subject of this formula : C = 10 + 2dd = (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

25. 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?

26. Level 7 Success 1. 3 days 2. 5 days 3. 3 days 4. 5 days

27. 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

28. 1) £35 2) C = 50 + 30d 3) d = (C – 100) ÷ 20 4 days