Thirty nine, seventy five
Problem
We have exactly $100$ coins. There are five different values of coins.
We have decided to buy a piece of computer software for £39.75. We have the correct money, not a penny more, not a penny less!
Can you discover what the five different types of coins are worth and how many of each we have saved?
Getting Started
We have the following numbers of the different value coins:
$46$, $23$, $14$, $10$ and $7$
But what are they?
All but one type of coin has a value that is a multiple of five.
Student Solutions
Thank you for working out the money in our birthday present pot! We have had lots of suggestions from St Aldhelms School:
Matthew:
| 20 * £1.00 | = | £20.00 |
| 20 * 50p | = | £10.00 |
| 44 * 20p | = | £8.80 |
| 3 * 10p | = | 30p |
| 13 * 5p | = | 65p |
| Total | £39.75 |
Justin:
| 7 * £1.00 | = | £7.00 |
| 48 * 50p | = | £24.00 |
| 43 * 20p | = | £8.60 |
| 1 * 10p | = | £0.10 |
| 1 * 5p | = | £0.05 |
| Total | £39.75 |
Emma:
| 10 * £1.00 | = | £10.00 |
| 50 * 50p | = | £25.00 |
| 10 * 20p | = | £2.00 |
| 25 * 10p | = | £2.50 |
| 5 * 5p | = | 25p |
| Total | £39.75 |
Daniel from Ysgol Dyffryn Dulas Corris found an other possible combination:
Daniel:
| 1 * £1.00 | = | £1.00 |
| 72 * 50p | = | £36.00 |
| 8 * 20p | = | £1.60 |
| 4 * 10p | = | 40p |
| 15 * 5p | = | 75p |
| Total | £39.75 |
When you pay for things in shops you can give the money in lots of different ways, but in this case you had exactly 100 coins. Perhaps it is a little unexpected that there are all these different solutions. Are there any more?