To determine the number of girls in the 7th grade at GACA based on the given ratio of boys to girls (2 to 4), we first need to express the ratio in terms of proportions.
The ratio of boys to girls is 2 to 4, which can be simplified to 1 to 2. This means for every 3 students (1 boy and 2 girls), there are a total of 3 parts in this ratio.
Total Parts:
- Boys: 2 parts
- Girls: 4 parts
- Total: 2 + 4 = 6 parts
Proportion Set Up:
Now, if we let \( x \) represent the number of girls, we can set up the proportion based on the total number of students (850):
\[ \frac{\text{Number of girls}}{\text{Total students}} = \frac{4 \text{ (parts for girls)}}{6 \text{ (total parts)}} \]
Thus, our proportion looks like this:
\[ \frac{x}{850} = \frac{4}{6} \]
Solving for \( x \):
Now we can solve for \( x \):
Cross-multiply to get:
\[ x \cdot 6 = 850 \cdot 4 \]
Calculating the right side:
\[ x \cdot 6 = 3400 \]
Now, divide both sides by 6 to find \( x \):
\[ x = \frac{3400}{6} \approx 566.67 \]
Since the number of students must be a whole number, we round to the nearest whole number:
\[ x \approx 567 \]
Conclusion:
You would expect approximately 567 girls in the 7th grade at GACA.
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