math

You received a $100 gift certificate to a clothing store. The store sells t-shirts for $15 and dress shirts for $22. You want to spend no more than the amount of the gift certificate. You want to leave at most $10 of the gift certificate unspent. You need at least one dress shirt What are all of the possible combinations of t-shirts and dress shirts you can buy?

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  1. If you spend $x, you want
    90 <= x <= 100
    so, if you buy m T-shirts and n dress shirts, you need
    15m+22n = x
    n >= 1
    So, start checking:
    with n=1, 15m+22 = x
    n m x
    1 5 22+15*1=97
    2 3 44+15*3=89; 44+15*4=104 so 2 dress shirts will not work.
    ...

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