Compare how much foreign currency each option delivers for the same starting budget. When a fee is deducted before exchange, subtract it from the starting amount and apply the quoted rate to the remainder. Set the two outputs equal to find where the offers tie.
The 2027 SEC G3 Mathematics K310 syllabus names money exchange as a possible real-world context. This example uses invented rates to show how a fixed fee and a better rate affect small and large exchanges.
- Check which currency the rate and fee use.
- Subtract a fee paid from the starting budget before converting.
- Compare the resulting foreign currency amounts.
- Check whether the question asks for a tie or a strict advantage.
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Write an expression for each offer
Let x be the total budget in Singapore dollars. Offer A gives 0.600 foreign currency units per Singapore dollar with no fee, so it delivers 0.600x units.
Offer B gives 0.625 foreign currency units per Singapore dollar and deducts an 8-dollar fee from the budget before exchanging the rest. Its output is 0.625(x − 8) for budgets of at least 8 dollars.
Put the fee inside the brackets because the remaining Singapore dollars are converted. Both output expressions are measured in foreign currency units.
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Worked example | Find the amount where the offers tie
Set 0.600x = 0.625(x − 8). Expanding gives 0.600x = 0.625x − 5. Rearranging gives 0.025x = 5, so the tie occurs at 200 Singapore dollars.
| Budget in SGD | Offer A | Offer B |
|---|---|---|
| 100 | 60.00 units | 57.50 units |
| 200 | 120.00 units | 120.00 units |
| 300 | 180.00 units | 182.50 units |
Offer B gains 0.025 units per Singapore dollar compared with A. At 200 dollars that gain reaches 5 units, exactly offsetting the loss of 0.625 × 8 units caused by the fee.
For budgets above 200 dollars, B gives more. Below 200 dollars, A gives more wherever both offers are available.
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Practise with a strict condition
If the budget must be a whole number of Singapore dollars and B must give strictly more than A, the smallest qualifying budget is 201 dollars. At 200 the two amounts are equal.
For a budget of 201 dollars, the unrounded amounts are 120.600 units for A and 120.625 for B. If an exam question specifies a rounding rule or cash denomination, apply it at the stage directed.
If a fee is stated in the foreign currency and deducted after conversion, its units match the output. In that case subtract it from the converted amount.
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Frequently asked questions
When do I divide by a quoted rate?
Divide when the rate gives starting currency per one unit of target currency. Multiply when it gives target currency per one unit of starting currency.
Does the higher rate always win?
With a fixed fee, compare the total output after deducting the fee as described in the question.
How can I check my break-even value?
Substitute it into both original expressions and confirm that the outputs match.
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