# Question 41f6d

Jan 15, 2017

The most apparent solution is 20% for the first discount, then 25% for the other discount.

#### Explanation:

The process for finding a solution is as follows:

There are infinite solutions, if we consider all rational numbers as possible prices. Picking a percentage for the first discount, let's say a%, since $\frac{1}{50}$ is 2%#, we find that the price after the first discount is $50 - \frac{a}{2}$ dollars. This means that $0 < a < 40$. If the resulting price is $p$ (after the first discount), we need to find what percentage the second discount is, so that the final price is $30$. If the second percentage is $b$, then $b = 100 \frac{p - 30}{p}$, or:

$100 \frac{50 - \frac{a}{2} - 30}{50 - \frac{a}{2}} = 100 \frac{40 - a}{100 - a}$.

Since $0 < a < 40$, a $b$ is always defined. So there are indeed infinite solutions.