In Germany, VAT is at 19%. Jeremy buys a calculator ain germany for 58.31Euro . This price includes VAT. Find the amount of VAT paid by Jeremy

so, he paid 58.31 €, and that includes the 19% of VAT, well, if the price was hmmm say "x", then that means the price is say the 100%, and the the VAT gets slapped on top of it... so whatever "x" is, the VAT is 19% of that.

therefore, "x" + VAT, which is 58.31 €, is really the 100% + 19%, or 119% of "x".

now if we know that 58.31 is 119%, and "x" is the 100%, what the dickens is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 58.31&119\\ x&100 \end{array}\implies \cfrac{58.31}{x}=\cfrac{119}{100}\implies \cfrac{58.31\cdot 100}{119}=x \\\\\\ 49=x[/tex]

ahhha, so the original price of the calculator was 49 €, what's the VAT?  well, 58.31 - x.