A shop sells 5 pairs of shoes at 10% off for a total of 4,500 baht. What was the original price of one pair of shoes?

Step-by-step solution

1. 1

   Reduce the total to a single item first. The 4,500 baht covers $5$ pairs of shoes, so the discounted price of one pair of shoes is

   $\frac{4500}{5}=900\ \text{baht}$

   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 $10\%$ means the customer still pays $90\%$ of the original price $x$:

   $x-\frac{10}{100}x=\left(1-\frac{10}{100}\right)x=\tfrac{9}{10}\,x$

3. 3

   Set up and solve the equation.

   $\tfrac{9}{10}\,x=900\quad\Longrightarrow\quad x=900\div\tfrac{9}{10}=1000\ \text{baht}$

   $\boxed{1000\ \text{baht per pair of shoes}}$

4. 4

   Check by applying the discount forwards. $10\%$ of $1000$ is $100$, so the sale price is $1000-100=900$ baht, and $5$ of them cost $5\times900=4,500$ baht — exactly the amount given.

5. 5

   Avoid the classic trap. Adding $10\%$ back onto the sale price does not undo the discount: $900\times1.10=990$ baht, which is short of $1000$. Percentages are taken of different bases going down (the original) and coming back up (the sale price), so the reverse operation is division by $0.90$, not multiplication by $1.10$.