€9.31
total = price + tax
... tax = 0.19×price . . . . . . . meaning of 19% VAT
... total = price + 0.19×price = 1.19×price
Dividing by 1.19, we can find the price in terms of the total.
... total/1.19 = price
And we can use this to find the tax
... tax = 0.19×price = 0.19×(total/1.19) . . . . . substitute for price
... tax = 0.19/1.19 × total = 19/119 × total . . . . . . simplify
... tax = 19/119 × 58.31 . . . . . . . put in total amount
... tax = 9.31 . . . . euros