# Strong induction

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Suppose that a store offers gift certificates in denominations of25 dollars and 40 dollars. Determine the possible total amounts you can form using these gift certificates.

Prove your answer using strong induction.

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##### Solution Summary

Strong induction is integrated.

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It's an old problem, and the answer is that any amount above $140, which is divisible by 5 is available in gift certificates in 25 and 40 dollars.

The basis for the induction can start from $140, but let's determine all possible values of the expression 25x+40y below 160:

x ...

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