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This week the topic was mathematics and money, and how maths is used in finance. We interviewed Sarah O’Rourke, who’s an accountant working on the problem of moving cash around to where it’s needed in cash machines. We discussed the ways she uses mathematical modelling to predict where demand for cash will be high, and also the other types of work that accountants do, and the different ways to become an accountant.

Interesting links:

• Accounting on Wikipedia
• Double entry bookkeeping at Dummies.com
• What is Financial Mathematics? at Plus Magazine
• Maths games - percentages at IXL
• Tax Matters at HMRC
• Money Talks, interactive game at the NI Curriculum website

Puzzle:

1. Using only £20 and £50 notes, what’s the largest multiple of £10 you can’t make?
2. In an imaginary scenario where the only notes are £30 and £70, again what’s the largest multiple of £10 you can’t make?
3. Why do you think we use the denominations of currency that we do use?

Solution:

1. Using only £20 and £50 notes, it’s not possible to make £10 or £30, but all other multiples of £10 are possible. This can be proven by noting that £20 x 2 = £40, and £50 x 1 = £50, and from here every other multiple of £10 can be made by adding different numbers of £20 to either of these base amounts.

2. If our notes are £30 and £70, we can’t make £50, £80 or £110, but all other multiples of £10 above £110 are possible. This can be proven by noticing that once you can make three consecutive multiples of £10, any other can be obtained by adding £30 notes - and in this case, we can make £120 = 4 x £30, £130 = £70 + 2 x £30, and £140 = 2 x £70 so we can then get £150, £160 and £170 by adding £30 to each, and so on.

3. The notes currently in use (£5, £10, £20 and (rarely) £50) have been chosen so that it’s possible to make any amount that’s a multiple of £5 using relatively few notes. We don’t need a £30, as it can be made easily using £10 + £20. The system is designed to make it as easy as possible to make any amount, while keeping the number of different types of note needed relatively small.

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