Question #41f6d

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Question #41f6d

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Answer 1 · 2017-01-15T00:28:19

The most apparent solution is $20 %$ $20%$ for the first discount, then $25 %$ $25%$ 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 $a %$ $a%$ , since $\frac{1}{50}$ $1/50$ is $2 %$ $2%$ , we find that the price after the first discount is $50 - \frac{a}{2}$ $50 - a/2$ dollars. This means that $0 < a < 40$ $0 < a < 40$ . If the resulting price is $p$ $p$ (after the first discount), we need to find what percentage the second discount is, so that the final price is $30$ $30$ . If the second percentage is $b$ $b$ , then $b = 100 \frac{p - 30}{p}$ $b = 100(p-30)/p$ , or:

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

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

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Question #41f6d

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