A 400 g jar costs 3.20 and a 600 g jar costs 4.50. Which is better value per gram? [3 marks]

With 1 = \1.40, convert\pounds 90$ to dollars. [2 marks]

With 1 = x20AC1.20, convert x20AC96 to pounds. [2 marks]

SQA SQA N5 Apps style-style practice: Washing powder is sold as a 750 g box for 4.50, a 1.2 kg box for 6.60, or a 2 kg box for 11.60. Which box is the best value? Justify your answer.

Compare the cost per gram (or per kilogram) for each box. Small box: 4.50 750 = 0.006 per gram, that is 0.6p per gram (1 mark). Medium box: 6.60 1200 = 0.0055 per gram, 0.55p per gram (1 mark). Large box: 11.60 2000 = 0.0058 per gram, 0.58p per gram (1 mark). The medium 1.2 kg box is the best value at 0.55p per gram (1 mark). Markers reward a consistent unit cost for each box and a justified conclusion. Compare in the same units throughout.

ScotlandApplications of MathematicsSyllabus dot point

How do you determine the best deal from several options and convert between currencies in both directions?

Determining the best deal given several pieces of information by comparing unit costs or total costs, and converting between currencies using an exchange rate in both directions.

A focused answer to the SQA National 5 Applications of Mathematics finance content on best deal and currency, covering comparing several offers by unit cost or total cost to find the best value, and converting between currencies in both directions using a given exchange rate.

Generated by Claude Opus 4.811 min answerUpdated 2026-06-15

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Determining the best deal
Converting currency
Examples in context
Try this

What this dot point is asking

The SQA wants you to compare several offers and decide which is the best deal, justifying your choice, and to convert between two currencies in both directions using a given exchange rate.

Determining the best deal

Best-deal questions give several offers and ask which is the best value. They cannot be compared directly because the sizes or quantities differ, so reduce each to a common measure first.

Compare two offers by unit cost

A $500$ g pack costs $\pounds 2.00$ and a $750$ g pack costs $\pounds 2.70$ . Determine which is better value.

Step 1: Find the unit cost for each pack

Because the packs differ in size, a direct price comparison is meaningless. Dividing the price by the quantity gives a common measure, cost per gram, so the two offers can be compared fairly:

500 \text{ g pack: } 2.00 \div 500 = \pounds 0.004 \text{ per gram}

750 \text{ g pack: } 2.70 \div 750 = \pounds 0.0036 \text{ per gram}

Step 2: Choose the lower unit cost and justify

The $750$ g pack costs $\pounds 0.0036$ per gram compared with $\pounds 0.004$ for the $500$ g pack. The $750$ g pack is cheaper per gram, so it is the better value.

Final answer: The $750$ g pack is better value at $\pounds 0.0036$ per gram.

Always compare in the same units, and state the conclusion with its reason; the SQA awards a mark for the justified decision, not just the arithmetic.

Best-deal questions are not always about packs of food. They might compare two mobile phone tariffs, two car-hire offers, or two ways of buying tickets, where the cheapest total for the same usage wins. When the offers include a fixed charge plus a rate, work out the full cost for the quantity in the question. For example, one tariff at $\pounds 10$ plus $5$ p per minute and another at $\pounds 15$ with free minutes can only be compared by costing the actual number of minutes used.

Converting currency

A currency conversion uses an exchange rate, such as $\pounds 1 = \$ 1.30$. The direction of the calculation decides whether you multiply or divide.

Convert in both directions

The exchange rate is $\pounds 1 = \unicode{x20AC}1.15$ . Convert $\pounds 200$ to euros, then convert $\unicode{x20AC}69$ back to pounds.

Step 1: Convert pounds to euros by multiplying

When converting from pounds to the currency named on the right-hand side of the rate, multiply by the rate. One pound buys $1.15$ euros, so two hundred pounds buys $200$ times as many:

200 \times 1.15 = \unicode{x20AC}230

Step 2: Convert euros to pounds by dividing

To reverse the direction, divide by the rate. Dividing undoes the multiplication: every $1.15$ euros was worth $\pounds 1$ , so the number of pounds is the euro amount divided by the rate:

69 \div 1.15 = \pounds 60

A sense-check helps: because $\pounds 1$ buys more than one euro, a euro amount should convert to a smaller number of pounds, which is exactly what happens here ( $69$ euros becomes $\pounds 60$ ).

Final answer: $\pounds 200 = \unicode{x20AC}230$ ; $\unicode{x20AC}69 = \pounds 60$ .

The key is the direction. Going to the currency named after the equals sign multiplies; coming back to pounds divides. A quick sense-check helps: if $\pounds 1$ buys more than one unit of the foreign currency, then a sum in pounds becomes a larger number of the foreign currency, and a foreign sum becomes a smaller number of pounds. Some questions also charge a commission or fee on the exchange, which is subtracted before or after converting, so read carefully to see when the fee applies.

Examples in context

These skills are everyday finance. A shopper compares packs of different sizes to find the cheapest per unit; a holidaymaker changes pounds into euros for a trip and back again on return; a business chooses the cheapest supplier by unit cost. Each rests on a fair comparison on a common basis, or applying an exchange rate the right way round, the skills here.

Try this

Q1. A $400$ g jar costs $\pounds 3.20$ and a $600$ g jar costs $\pounds 4.50$ . Which is better value per gram? [3 marks]

Cue. $0.008$ vs $0.0075$ per gram, so the $600$ g jar.

Q2. With $\pounds 1 = \$ 1.40 $, convert$ \pounds 90$ to dollars. [2 marks]

Cue. $90 \times 1.40 = \$ 126$.

Q3. With $\pounds 1 = \unicode{x20AC}1.20$ , convert $\unicode{x20AC}96$ to pounds. [2 marks]

Cue. $96 \div 1.20 = \pounds 80$ .

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA N5 Apps style4 marksWashing powder is sold as a

750

g box for

\pounds 4.50

, a

1.2

kg box for

\pounds 6.60

, or a

2

kg box for

\pounds 11.60

. Which box is the best value? Justify your answer.

Show worked answer →

Compare the cost per gram (or per kilogram) for each box. Small box: $\pounds 4.50 \div 750 = \pounds 0.006$ per gram, that is $0.6$ p per gram (1 mark). Medium box: $\pounds 6.60 \div 1200 = \pounds 0.0055$ per gram, $0.55$ p per gram (1 mark). Large box: $\pounds 11.60 \div 2000 = \pounds 0.0058$ per gram, $0.58$ p per gram (1 mark). The medium $1.2$ kg box is the best value at $0.55$ p per gram (1 mark). Markers reward a consistent unit cost for each box and a justified conclusion. Compare in the same units throughout.

SQA N5 Apps style3 marksThe exchange rate is

\pounds 1 = \

1.25

. Convert

\pounds 240

to dollars, then convert

80

back to pounds.

Show worked answer →

To convert pounds to dollars, multiply by the rate: $240 \times 1.25 = \$ 300 $(1 mark). To convert dollars back to pounds, divide by the rate:$ 80 \div 1.25 $(1 mark). Evaluate:$ 80 \div 1.25 = \pounds 64$ (1 mark). Markers reward multiplying when going from pounds to dollars and dividing when going from dollars to pounds. Mixing up the two directions is the usual error.

Related dot points

Sources & how we know this

SQA National 5 Applications of Mathematics Course Specification — SQA (2023)
SQA National 5 Applications of Mathematics - Course overview and resources — SQA (2023)