Final answer:
To find the overall ratio for 3 servings of a dish with garlic, chilies, and eggs, we scale up the individual ratios and then combine them. The initial combined ratio for garlic (3:15), chilies (3:6), and eggs (3:27) is 9:48. After simplifying it by dividing both terms by their GCD, which is 3, we obtain the final overall ratio of 1:16.
Step-by-step explanation:
To solve the ratio problem for preparing 3 servings, we need to determine the overall ratio for garlic, chilies, and eggs. The ratios provided are for garlic 1:5, for chilies 1:2, and for eggs 1:9. Since we're looking at 3 servings, we'll need to multiply each part of the ratio by 3 to scale it appropriately.
For garlic, the ratio becomes 3:15. For chilies, it becomes 3:6. And for eggs, it becomes 3:27. The overall ratio combines these three separate ratios. To do that, we add up the respective parts of each ratio for the numerator and the denominator separately, which results in 3+3+3 for the numerator and 15+6+27 for the denominator. This gives us an overall ratio of 9:48 for the three ingredients combined.
However, it's often more useful to simplify the ratio. To simplify, we find the greatest common divisor (GCD) for both numbers, which in this case is 3. Therefore, by dividing both sides of the ratio by 3, we get the simplified overall ratio for garlic, chilies, and eggs to be 1:16.