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    Strong Induction and Gift Card Totals

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    Suppose that a store offers gift certificates in denominations of 25 dollars and 40 dollars. Determine the possible total amounts (below $160) you can form using these gift certificates.
    Prove your answer using strong induction.

    © BrainMass Inc. brainmass.com October 10, 2019, 5:35 am ad1c9bdddf
    https://brainmass.com/math/discrete-optimization/strong-induction-gift-card-totals-510423

    Solution Preview

    ** Please see the attached file for the complete solution **
    Proof. At first, the amounts seem semi-random. All possible combinations are:

    $25 certificates $40 certificates Total
    1 0 $25
    0 1 $40
    2 0 $50
    1 1 $65
    3 0 $75
    0 2 $80
    2 1 $90
    4 0 ...

    Solution Summary

    This solution uses strong induction to find every possible total amount using a combination of gift card values.

    $2.19