To solve the problem, we first need to understand the ratio of boys to girls, which is given as 2 to 4. This ratio can be simplified to 1 to 2, meaning for every 1 boy, there are 2 girls.
Next, we calculate the total parts in this ratio:
- 1 part (boys) + 2 parts (girls) = 3 parts total.
Now, we want to determine how many of the 850 students are girls. Since 2 parts out of 3 represent the girls, we can set up the following proportion:
\[ \text{Proportion of Girls} = \frac{2 \text{ parts}}{3 \text{ parts total}} = \frac{2}{3} \]
Now we can calculate the number of girls:
\[ \text{Number of girls} = \left(\frac{2}{3}\right) \times 850 = \frac{1700}{3} \approx 566.67 \]
Rounding to the nearest whole number, we expect there to be approximately 567 girls.
So for your questions:
- The correct proportion to use is \( \frac{2}{3} \).
- You would expect there to be 567 girls out of 850 students.
The correct response from your options is 567 girls out of 850 students.