2. At the Fruit Stand, the ratio of red apples to green apples is \( 2: 3 \). If the Fruit Stand has 57 green apples, how many red apples does it have?

To solve the problem, we start by understanding the ratio of red apples to green apples, which is \( 2: 3 \). This means that for every 2 red apples, there are 3 green apples. If there are 57 green apples, we can set up a proportion to find the number of red apples: Let \( r \) be the number of red apples. From the ratio, we can express this as: \[ \frac{r}{57} = \frac{2}{3} \] Cross-multiplying gives: \[ 3r = 2 \times 57 \] Calculating \( 2 \times 57 \) yields 114, so we have: \[ 3r = 114 \] Dividing both sides by 3 gives: \[ r = \frac{114}{3} = 38 \] Therefore, the Fruit Stand has **38 red apples**. Additionally, did you know that the theory of ratios has deep historical roots? Ancient civilizations, such as the Egyptians and Greeks, used ratios to solve practical problems, from building pyramids to dividing land. Ratios help us make sense of relationships in everything from nature to finance! What's more, this ratio concept finds its way into cooking, particularly in recipes! For instance, if you're baking a fruit pie, maintaining ratios of fruits together can lead to a perfectly balanced flavor. So next time you're whisking together ingredients, remember those red and green apples!