Final answer:
The ratio of Hamburgers to the total number of main dishes (Hotdogs and Hamburgers) at the cookout, with a given ratio of Hotdogs to Hamburgers of 10:7, is 7:17. The total number of main dishes is the sum of Hotdogs and Hamburgers, calculated as 17 times a common factor (x).
Step-by-step explanation:
The student asked about the ratio of Hamburgers to the total number of main dishes (Hotdogs and Hamburgers combined) at a neighborhood cookout, given that the ratio of Hotdogs to Hamburgers was 10:7. This is a mathematics problem involving ratios.
First, let's determine the total number of main dishes in terms of a common variable based on the given ratio. If we represent the number of Hotdogs by 10x and Hamburgers by 7x (where x is a common factor), the total number of dishes is 10x (Hotdogs) + 7x (Hamburgers) = 17x (total dishes).
We need to find the ratio of Hamburgers to total dishes, which is represented by 7x to 17x. Simplifying this ratio, we get:
- Hamburgers to total dishes = 7x / 17x = 7/17.
Therefore, the ratio of Hamburgers to the total number of main dishes on the grill is 7:17.