Select a card for each currency
An online shopper from Singapore (currency Singapore Dollar, symbol $) wants to purchase a watch, a ring and a pair of shoes from web portals based in France (Euro, €), UK (British Pound Sterling, £) and Japan (Japanese Yen, ¥) respectively using credit cards from three banks.
Each bank imposes foreign exchange rates depending on the currencies in which the purchases are made. Checks with the banks reveal that if she is to proceed with the purchases, she would incur total credit bills listed in the table below:
| Credit Card | € per dollar | £ per dollar | ¥ per dollar | Total bill in dollars |
|---|---|---|---|---|
| A | 0.5501 | 0.4895 | 67.0933 | 1154.92 |
| B | 0.5321 | 0.499 | 67.8542 | 1156.98 |
| C | 0.5674 | 0.491 | 65.045 | 1138.99 |
Given that she decides to purchase each of her items using the credit card which offers the most favourable exchange rate, determine the total expenditure for her purchases, to the nearest dollar. marks
[2011/TJC/J1/Lecture Test]
Solution
Exchange-rate modelling
An online shopper from Singapore wants to buy a watch from a French site (€), a ring from a UK site (£) and a pair of shoes from a Japanese site (¥), using credit cards from three banks. The banks' exchange rates (foreign currency per Singapore dollar) and the total bills in dollars if all three items were bought with that card are:
Card A: 0.5501 €, 0.4895 £, 67.0933 ¥ per $: $1154.92. Card B: 0.5321, 0.4990, 67.8542: $1156.98. Card C: 0.5674, 0.4910, 65.0450: $1138.99.
She uses, for each item, the card with the most favourable exchange rate. Determine the total expenditure to the nearest dollar.
Hint
Let , , be the prices in €, £ and ¥. Converting to dollars divides by the rate (€ per dollar).
Each card gives one equation. Solve for .
Then for each currency pick the largest rate (more foreign currency per dollar means a cheaper bill) and add up.
The rate is foreign currency per dollar. To get dollars, divide, not multiply.
A larger number of euros per dollar means each euro costs fewer dollars. The most favourable rate is the largest.
Each item can be bought with a different card, so choose per currency.
Answer · Q
1128 dollars (nearest dollar).
Convert prices into dollars
One Singapore dollar buys €0.5501, so a watch costing € costs dollars.
One equation per card
Each card has its own rates for all three currencies and its own total bill.
Solve
The graphing calculator's simultaneous-equation solver; keep full precision.
Best card for each currency
A larger rate means a cheaper dollar cost: euros: card C (), pounds: card B (), yen: card B ().
Total expenditure
Rounded to the nearest dollar, the total is $1128.
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