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Postage Stamps

Problem

A small village post office is selling 1st class stamps and 2nd class stamps in a book costing £1. If a 1st class stamp is 9p and a 2nd class stamp is 7p, how many ways can a £1 book be filled?


Solution

We are attempting to solve the Diophantine equation 9a + 7b = 100, of which there are two positive solutions:
1 times 9 + 13 times 7 = 100
8 times 9 + 4 times 7 = 100

How many solutions are there to the equation 4a + 3b = 100?
Try different equations and see if you can spot any patterns.

Problem ID: 58 (Dec 2001)     Difficulty: 1 Star

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