Everyday Money Problems
Work out bills made of a fixed charge plus a rate, find the hours, days or kilometres from a total, and handle hire charges and deposit plus instalment plans.
In the exam for Cambridge IGCSE Maths 0580, Cambridge O Level Maths 4024, Edexcel IGCSE Maths 4MA1 · 14 real past-paper questions below
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What Everyday Money Problems Are
Many bills have two parts: a fixed amount you always pay, and a rate for each hour, day or kilometre you use. Big buys can be paid in parts: a deposit now, then equal payments.
| Word | Meaning |
| Fixed charge | paid once, however much you use |
| Rate | the cost of one unit: one hour, day or kilometre |
| Tariff | the list of charges and rates |
| Deposit | the first payment, made at the start |
| Instalments | the equal payments after the deposit |
Key idea
Write money with two decimal places: three dollars fifty is $3.50, never $3.5.
A Fixed Charge Plus a Rate
The 2-mark question: a taxi, a gardener or a delivery charges a fixed amount plus so much for each unit. Find the total.
Formula
A taxi charges $3.50 plus $1.20 per kilometre. The journey is 9 km.
Worked example
- 1
— the distance part: units × rate
- 2
— add the fixed charge once
- 3
— the fare, with two decimal places
Common mistake
Leaving out the fixed charge, or adding it for every kilometre. It is added once, at the end.
Key idea
Free units come off first. A phone plan costs $12 a month and $0.05 a minute after 300 free minutes. For 380 minutes you pay for 80: .
Working Backwards: How Many Kilometres?
The 3-mark question gives the total bill and asks for the hours, days or kilometres. Undo the bill in reverse order.
Car hire costs $40 per day plus $0.25 per kilometre. Sam hires a car for 5 days and pays $312. How far does he drive?
Worked example
- 1
— the daily part first: it does not depend on distance
- 2
— money left was for the kilometres
- 3
— divide by the rate for one kilometre
- 4
— check: 200 + 448 × 0.25 = 312
Rule
Take off the fixed part first. Then divide what is left by the rate.
Common mistake
Dividing the whole $312 by 0.25. The $200 for the days was not for kilometres.
First Day, Then Each Extra Day
The 3-mark question: a hire shop charges one price for the first day and a lower price for each extra day.
A machine costs $24.50 for the first day and $12.75 for each extra day.
Worked example
- 1
— extra days are the days after the first
- 2
— first day, plus the extra days
- 3
— the cost for 4 days
Backwards: Lina pays $88.25. How many days?
Worked example
- 1
— take off the first day
- 2
— extra days
- 3
— add the first day back
Common mistake
Answering 5 days. That counts only the extra days. Add the first day back on.
Deposit and Instalments
The 3-mark question: pay a deposit, then equal monthly payments. Find the total, the extra cost, or the number of payments.
Formula
n is the number of payments and p is the amount of each one.
A bicycle costs $480 cash, or $100 deposit and 12 monthly payments of $36. How much more is the instalment plan?
Worked example
- 1
— the monthly payments
- 2
— add the deposit
- 3
— the extra cost of paying in parts
How many payments? A laptop costs $840. Ali pays $120 deposit, then $45 a month.
Worked example
- 1
— still to pay after the deposit
- 2
— 16 monthly payments
Common mistake
Forgetting the deposit. The payments alone are $432, but the plan costs $532.
Key idea
If the deposit is a fraction or a percentage of the price, work it out first. One fifth of a $720 price is $144.
Which Method? Read the Question
Look at how the charge is made, and at what the question asks you to find.
| You see | You do |
| $5 plus $1.50 per km | fixed + rate × units |
| Total given, find the hours or km | take off the fixed part, then divide |
| First day, then each extra day | extra days = days − 1 |
| Deposit and monthly payments | deposit + number × payment |
| How many payments? | price − deposit, then divide |
| Pay per hour or overtime | Earnings and Deductions |
| Change, offers or best buy | Earnings and Deductions |
| Deposit of 15% | Calculating a Percentage of a Quantity |
| Interest on a loan | Simple Interest |
| Bought and sold | Profit and Loss |
Key idea
Check your answer: a number of days or payments is a whole number, and it should give back the total in the question.
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