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The multi-choice question, for revision for 12 year olds, is here:

A company exchanges foreign currency. They offer $\$1.5$ for each pound. On top of this, they charge a fee of $£4.50$. Which formula shows the cost, $C$, in pounds of purchasing $\$D$? $${C = \frac{D}{1.5} + 4.5}$$ $${C = \frac{1.5}{D} + 4.5}$$ $${C = \frac{D}{1.5} + 450}$$

This seems considerably more complicated than the rest of the questions, in my opinion. But anyway, I would start by saying -

$${D = {1.5}C - 4.5}$$ ... which is equivalent to $${C = \frac{D + 4.5}{1.5}}$$ ... or more neatly $${C = \frac{2D}{3} + 3}$$ ... which is not one of the answers. The question is: is my mathematics flawed, or the BBC's?

Party Ark
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  • The first one is correct. They charge $$1.5$ per pound so it is $\frac{1}{1.5}$ pounds per dollar. Multiplying that rate by $D$ dollars gives $\frac{D}{1.5}$ pounds plus a fixed cost of 4.5 gives the answer. – John Douma Apr 18 '16 at 17:18
  • Well, let's ask a specific question: how many pounds do I need to get exactly $$1.5$? That is easily solved: I need $1$ for the conversion and $4.5$ for the fee, thus $5.5$. Your formula does not give that answer. – lulu Apr 18 '16 at 17:18
  • Thank you, I'm still confused. If I start with £100 I'll get ($150 - $4.50) = $145.50. And, reversing it, (($145.50 x 2) / 3 ) + 3 gets me back to the £100. – Party Ark Apr 18 '16 at 17:24
  • Ah, I see the problem. The fee is £4.50 not $4.50. Back to the drawing board! – Party Ark Apr 18 '16 at 17:26

1 Answers1

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If you use units (the exchange rate is $R = 1.5 \$ / 1£$ and the additional cost is $A = 4.5£$), you will see that the correct formula is $D = R (C - A) $.

In words, from the paid amount $C $ (the cost), the bank keeps the additional cost $A = 4.5£$ and exchanges the rest for the given exchange rate $R $.

Now rearranging will yield the first solution.

Different way of looking at it. You want to get $D $ dollars. This will normally cost you $D/R $ pounds (check the units!). But finally, the bank cares an additional fee of $A = 4.5 £$, so that we need to pay $4.5 £ + D /R $.

PhoemueX
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