The first discount on a camera was 18%. The second discount was 20%. After the two discounts the price became $328. What was the original price?
The Correct Answer and Explanation is:
To find the original price of the camera before the two successive discounts, we work backwards from the final price of $328.
Step-by-step Solution:
Let the original price be x.
- First discount is 18%, so the price after the first discount is: x×(1−0.18)=x×0.82x \times (1 – 0.18) = x \times 0.82
- Second discount is 20%, applied to the discounted price: (x×0.82)×(1−0.20)=x×0.82×0.80(x \times 0.82) \times (1 – 0.20) = x \times 0.82 \times 0.80
- The final price is given as $328, so: x×0.82×0.80=328x \times 0.82 \times 0.80 = 328
- Simplify the multiplication: x×0.656=328x \times 0.656 = 328
- Solve for x: x=3280.656=500x = \frac{328}{0.656} = 500
✅ Correct Answer: $500
Explanation
To determine the original price before successive discounts, it’s crucial to understand how percentage reductions apply one after the other. These aren’t simply additive. That is, an 18% discount followed by a 20% discount does not equal a 38% total discount, because the second discount is applied to a reduced price, not the original.
Start by letting the original price be x. After an 18% discount, you’re paying 82% of the original price — hence, we multiply x by 0.82. This gives us the intermediate discounted price.
Next, a 20% discount is applied to this reduced price. Paying 80% of that means we multiply by 0.80. The cumulative effect of both discounts is therefore 0.82 × 0.80 = 0.656, meaning the customer ends up paying 65.6% of the original price.
We’re told that the final price after both discounts is $328. So we can write: 0.656×original price=3280.656 \times \text{original price} = 328
Solving for the original price involves dividing $328 by 0.656, which gives $500.
This method illustrates how percentages multiply, not add, when applied sequentially. It’s a common misconception to simply add percentages, but successive percentage changes always apply to a changing base. Working backward using multiplication and division helps reverse the discounts accurately and find the original price.
