Question

Question #41f6d

Answer 1

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 `1/50` is `2%`, we find that the price after the first discount is `50 - 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(p-30)/p`, or:

`100(50-a/2-30)/(50-a/2) = 100(40-a)/(100-a)`.

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