I suggest that you offer the 12-year-old the regula falsi method. In this method, you guess, check if the guess is correct, and if it isn't, you adjust the guess.
Let's try a slightly different problem:
A hat now costs €6.39 after a 10% reduction. How much was it originally?
The original price must have been a little more than €6.39, so we begin by guessing that it was around €7 before. But 10% of €7 is €0.70, so had it been €7 before, the price after reduction would be $€7 - €0.70 = €6.30$. This is too small by €0.09. €0.09 is small, so we must be very close. What increase in the original price would cause the discounted price to increase by €0.09? It must be a bit more than €0.09, so try increasing the supposed original price by €0.10, to €7.10. On checking, this is in fact the answer.
This method is self-correcting. Suppose the 12-year-old tried increasing the guess by €0.20, to €7.20. This would give a discounted price of $€7.20 - €0.72 = €6.48$, which is too high. So the correct answer must be somewhere between €7.00 and €7.20.