# 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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