Select a card for each currency · source reference

Printed question

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. [5]

[2011/TJC/J1/Lecture Test]

Printed working

Let €$x$, £$y$, ¥$z$ be the cost of the watch, ring and shoes respectively.

Card A: $\frac{x}{0.5501}+\frac{y}{0.4895}+\frac{z}{67.0933}=1154.92$ — (1).

Card B: $\frac{x}{0.5321}+\frac{y}{0.4990}+\frac{z}{67.8542}=1156.98$ — (2).

Card C: $\frac{x}{0.5674}+\frac{y}{0.4910}+\frac{z}{65.0450}=1138.99$ — (3).

Using the GC, $x=250.06,y=341.83,z=135.02$.

Total expenditure

$$=\frac{250.06}{0.5674}+\frac{341.83}{0.4990}+\frac{135.02}{67.8542}$$

$=1127.74$ dollars $\approx1128$ dollars (nearest dollar).

Teacher notes

The cost of watch is €$x$. Using credit card A, the exchange rate is €0.5501 per dollar $\Rightarrow\frac1{0.5501}$ dollars per €. Thus cost of watch in dollars is $\frac{x}{0.5501}$ dollars. Similar for the other cards and currencies.

Most favourable exchange rate (per dollar) is the one with the highest value.

Printed answer key

1128 dollars (nearest dollar).

Source provenance

2025 TJC H2 Math (9758) JC2 MSM: EQUATIONS. Question sheet printed pages 15–19; solution sheet printed pages 1–12. Original exam attribution is retained above. Currency dollar signs are spelled out outside maths to avoid confusing currency with TeX delimiters.