A shop sells 6 watches at 15% off for a total of 10,200 baht. What was the original price of one watch?

Step-by-step solution

1. 1

   Reduce the total to a single item first. The 10,200 baht covers $6$ watches, so the discounted price of one watch is

   $\frac{10200}{6}=1700\ \text{baht}$

   Keeping the quantity in the equation until the end only makes the algebra heavier.

2. 2

   Express the sale price as a fraction of the original. A discount of $15\%$ means the customer still pays $85\%$ of the original price $x$:

   $x-\frac{15}{100}x=\left(1-\frac{15}{100}\right)x=\tfrac{17}{20}\,x$

3. 3

   Set up and solve the equation.

   $\tfrac{17}{20}\,x=1700\quad\Longrightarrow\quad x=1700\div\tfrac{17}{20}=2000\ \text{baht}$

   $\boxed{2000\ \text{baht per watch}}$

4. 4

   Check by applying the discount forwards. $15\%$ of $2000$ is $300$, so the sale price is $2000-300=1700$ baht, and $6$ of them cost $6\times1700=10,200$ baht — exactly the amount given.

5. 5

   Avoid the classic trap. Adding $15\%$ back onto the sale price does not undo the discount: $1700\times1.15=1,955$ baht, which is short of $2000$. Percentages are taken of different bases going down (the original) and coming back up (the sale price), so the reverse operation is division by $0.85$, not multiplication by $1.15$.