I'm visiting an unfamiliar state. This state has a sales tax of 6.1% but I don't know this. All I know is the tax rate is of the form a.b% where a and b are single digits.

I buy an item at a store and am able to deduce the tax rate from the item's price and the tax amount as listed on the receipt.

What is the minimum cost of the item that would allow me to make such a deduction?

Note: The tax amount listed on the receipt is rounded to the nearest cent.

If I buy an item costing $10, then the amount of tax will be distinct for every possible tax rate of the given type.

If I buy an item costing, say, $9, and the tax charged is, say, 0.5, then the tax rate could be either 0.6% or 0.5%; and if the tax charged is, say, 0.86, then the tax rate could be either 9.6% or 9.5%.

As I interpret the problem, the solution is therefore $10.

But smaller solutions are possible if the rate happens to be helpful. For example if I pay $6 and the tax amount is 56c, then the tax rate is 9.4%, since a rate of 9.5% translates into tax of 57c, while a rate of 9.3% translates into 55c.

$6 seems to be the smallest dollar figure that at least sometimes produces unique solutions in this this type. If fractions of a dollar are allowed then a cost of $5.43 gives a unique tax rate of 9.4%.

Edited on August 22, 2018, 9:23 am

Posted by broll on 2018-08-22 09:07:18