Question: A store sells a laptop for $1200 after a 25% discount. The store initially purchased the laptop for $800.
a) What was the original price before the discount?
1. **State the problem:**
We know the selling price after a 25% discount is $1200. We want to find the original price before the discount.
2. **Formula used:**
If the original price is $P$, then after a 25% discount, the price becomes:
$$ P - 0.25P = 0.75P $$
3. **Set up the equation:**
The discounted price is given as $1200$, so:
$$ 0.75P = 1200 $$
4. **Solve for $P$:**
Divide both sides by $0.75$:
$$ P = \frac{1200}{0.75} $$
Show cancellation:
$$ P = \frac{1200}{\cancel{0.75}} \times \frac{\cancel{1}}{1} $$
Calculate:
$$ P = 1600 $$
5. **Interpretation:**
The original price before the discount was $1600$.
6. **Additional info:**
The store purchased the laptop for $800$, so the profit margin can be calculated if needed, but the question only asks for the original price before discount.