A shop sells 8 shirts at 25% off for a total of 9,600 baht. What was the original price of one shirt?

Step-by-step solution

1. 1

   Reduce the total to a single item first. The 9,600 baht covers $8$ shirts, so the discounted price of one shirt is

   $\frac{9600}{8}=1200\ \text{baht}$

   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 $25\%$ means the customer still pays $75\%$ of the original price $x$:

   $x-\frac{25}{100}x=\left(1-\frac{25}{100}\right)x=\tfrac{3}{4}\,x$

3. 3

   Set up and solve the equation.

   $\tfrac{3}{4}\,x=1200\quad\Longrightarrow\quad x=1200\div\tfrac{3}{4}=1600\ \text{baht}$

   $\boxed{1600\ \text{baht per shirt}}$

4. 4

   Check by applying the discount forwards. $25\%$ of $1600$ is $400$, so the sale price is $1600-400=1200$ baht, and $8$ of them cost $8\times1200=9,600$ baht — exactly the amount given.

5. 5

   Avoid the classic trap. Adding $25\%$ back onto the sale price does not undo the discount: $1200\times1.25=1,500$ baht, which is short of $1600$. Percentages are taken of different bases going down (the original) and coming back up (the sale price), so the reverse operation is division by $0.75$, not multiplication by $1.25$.