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Cambridge IGCSE0580

Money

Mathematics 0580 Chapter Notes

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Money
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Money notes

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In this chapter

  1. 1Calculating with money
  2. 2Bills, totals and missing values
  3. 3Changing one currency into another
  4. 4Two conversions in a row
  5. 5Comparing prices and rounding

1. Calculating with money

Money questions use the four operations on decimals. Read the whole question, then work in stages: find each cost, add the costs, then take the total from the amount paid.

Change cents and dollars to one unit first: 100 cents = textdollar1.

cost = price each × number bought

change = amount paid - total cost

Examiner insight

“Errors often resulted from reading the question incorrectly or ignoring the mixture of cents and dollars in the data.”

Worked example 13 marks

A café charges textdollar5.75 for a cake and textdollar4.40 for a milkshake.

Sue buys 3 cakes and 2 milkshakes.

Work out how much change she receives from a textdollar50 note.

  1. 1

    cakes and milkshakes: 3 × 5.75 = 17.25 and 2 × 4.40 = 8.80 [1]

  2. 2

    total cost = 17.25 + 8.80 = textdollar26.05 [1]

  3. 3

    change = 50 - 26.05 = textdollar23.95 [1]

2. Bills, totals and missing values

A shopping bill has a cost per unit, a quantity and a total on each line. Find a missing total by multiplying. Find a missing quantity or price by taking the known lines away from the final total, then dividing by the quantity or price you know.

total = cost per kg × number of kg

cost per kg = total ÷ number of kg

Worked example 13 marks

The table shows a shopping bill for three items.

Complete the table.

itemcost per kgnumber of kgtotal
potatoestextdollar2.183.5textdollar7.63
orangestextdollar1.486textdollar
onionstextdollar5.2textdollar
total costtextdollar29.25
  1. 1

    oranges: 1.48 × 6 = textdollar8.88 [1]

  2. 2

    onions total = 29.25 - 7.63 - 8.88 = textdollar12.74 [1]

  3. 3

    onions cost per kg = 12.74 ÷ 5.2 = textdollar2.45 [1]

3. Changing one currency into another

An exchange rate gives the value of one unit of a currency in another, such as textdollar1 = 0.93 euros.

To change money, multiply by the rate when you start from the currency that has 1 in the rate. Going the other way, divide by the rate.

Check the size of your answer. If each dollar is worth less than 1 euro, the amount in euros is smaller than the amount in dollars.

euros = dollars × 0.93

dollars = euros ÷ 0.93

Examiner insight

“Candidates should decide if the amount of money in euros is going to be numerically larger or smaller than 350.” “Candidates should look at the exchange rate to observe that since 1 > 0.84 the number of dollars should be greater than the number, 105, of euros.”

Worked example 12 marks

Kit and Jo are changing some money.

The exchange rate is textdollar1 = 0.93 euros.

(a) Kit changes textdollar350 into euros. Calculate the amount, in euros, that Kit receives.

(b) Jo changes 150 euros into dollars (textdollar). Calculate the amount, in dollars, that Jo receives.

  1. 1

    (a) dollars to euros, so multiply: 350 × 0.93 = 325.50 euros [1]

  2. 2

    (b) euros to dollars, so divide: 150 ÷ 0.93 = textdollar161.29 [1]

4. Two conversions in a row

Some questions give two rates, both tied to a middle currency. Convert to the middle currency first, then on to the one you want. Decide multiply or divide at each stage on its own.

When an exact amount of money is asked for, give the full value. Do not round it.

Examiner insight

“A few candidates multiplied 576 by 1.28 instead of dividing.”

Worked example 12 marks

The exchange rate between pounds (£) and dollars (textdollar) is £1 = textdollar1.28.

The exchange rate between pounds and rupees is £1 = 115 rupees.

A computer costs textdollar576.

Calculate the cost of the computer in rupees.

  1. 1

    dollars to pounds, so divide: 576 ÷ 1.28 = £450 [1]

  2. 2

    pounds to rupees, so multiply: 450 × 115 = 51 750 rupees [1]

5. Comparing prices and rounding

To compare two prices, change both into one currency. Give the answer in the currency the question asks for.

Keep the full calculator value between stages. Premature rounding at the conversion stage loses the accuracy mark. Round once, at the end.

Examiner insight

“Some lost accuracy by premature rounding at the conversion stage.” “However, when an exact amount of money is required, candidates should give the precise value without rounding.”

Worked example 12 marks

The price of a train ticket is either textdollar85 or 75 euros.

The exchange rate is 1 euro = textdollar1.18.

Calculate the difference between the two prices.

Give your answer in euros.

  1. 1

    dollars to euros: 85 ÷ 1.18 = 72.033… euros (not rounded) [1]

  2. 2

    difference = 75 - 72.033… = 2.966… = 2.97 euros [1]

Recap

  • Change = amount paid − total cost. Work in stages.
  • Cost = price each × number. Put cents and dollars in one unit.
  • Exchange rate: multiply from the currency with 1 in the rate, divide the other way.
  • Check whether the answer should be bigger or smaller than the start.
  • Two rates: go through the middle currency, one stage at a time.
  • Compare prices in one currency, the one asked for. Round once, at the end.
  • An exact amount of money is not rounded.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Do not use a calculator. A pen costs textdollar0.35. Sam buys 6 pens. How much does he pay?1 mark
  2. A notebook costs 85 cents and a ruler costs textdollar1.20. Work out the total cost in dollars.2 marks
  3. Do not use a calculator. Adult tickets cost textdollar8 and child tickets cost textdollar5. A family buys 2 adult tickets and 3 child tickets. They pay with a textdollar50 note. How much change do they get?3 marks
  4. Cakes cost textdollar3.40 each. Ria has textdollar20. Work out the maximum number of cakes she can buy and the change she receives.3 marks
  5. Do not use a calculator. The exchange rate is 1 euro = textdollar1.20. Change 50 euros into dollars.1 mark
  6. The exchange rate is textdollar1 = 0.93 euros. Change 280 euros into dollars. Give your answer correct to the nearest cent.2 marks
  7. Do not use a calculator. The exchange rate is textdollar1 = 80 rupees. A bag costs 2000 rupees and a belt costs 600 rupees. Work out the total cost in dollars.2 marks
  8. A jacket costs 95 euros in Paris and textdollar104 in Boston. The exchange rate is 1 euro = textdollar1.12. Where is the jacket cheaper, and by how much? Give the difference in dollars.3 marks
  9. Do not use a calculator. The exchange rates are £1 = textdollar1.25 and £1 = 120 rupees. A buyer in New York has textdollar500. She buys a rug from a trader in Delhi for 42 000 rupees and pays a delivery charge of 3000 rupees. Work out how many dollars she has left.4 marks
  10. A school in France needs 35 calculators. A shop in the USA sells them for textdollar13.80 each and charges 24 euros to deliver the whole order. A shop in France sells them for 12.50 euros each with free delivery. The exchange rate is 1 euro = textdollar1.18. Work out which shop is cheaper for the whole order, and by how much. Give your answer in euros, correct to the nearest cent.5 marks

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