how to determine if each pair of ratios form a proportion

A sweater is on sale for 52 dollars. If the original price was 78 dollars, what is the percent discount?

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To determine if each pair of ratios form a proportion, you need to compare the ratios and check if they are equal. Here's a step-by-step process:

1. Write down the two ratios you want to compare. For example, let's say you have the ratios 3:4 and 15:20.

2. Simplify both ratios. You can do this by dividing both sides of the ratio by their greatest common divisor (GCD). In our example, the first ratio simplifies to 3:4 and the second ratio simplifies to 3:4 as well.

3. Compare the simplified ratios. If the simplified ratios are the same, then the original ratios form a proportion. In our example, since the simplified ratios are identical (3:4), we can conclude that the original ratios do form a proportion.

Now, moving on to your next question:

To calculate the percent discount, you can use the following formula:

Percent discount = (Original price - Sale price) / Original price * 100

Let's use the given information to solve the problem:

Original price = $78
Sale price = $52

Percent discount = (78 - 52) / 78 * 100
Percent discount = 26 / 78 * 100
Percent discount = 0.3333 * 100
Percent discount = 33.33%

Therefore, the percent discount for the sweater is 33.33%.

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