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Thirty Nine, Seventy Five

Age 11 to 14
Challenge Level Yellow star
  • Problem
  • Getting Started
  • 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?

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Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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