To solve this problem, we first need to establish the proportion between the French and Spanish classes.
Let:
- \( F \) = number of French classes
- \( S \) = number of Spanish classes
From the problem, we know: \[ S = 3F \]
This means the ratio of Spanish classes to French classes is \( S:F = 3:1 \).
If we let the total number of students be 850, we can use this ratio to determine how many students are in each language.
The total ratio of students can be considered as: \[ F + S = 850 \]
Substituting \( S = 3F \) into the total gives: \[ F + 3F = 850 \] \[ 4F = 850 \] \[ F = \frac{850}{4} = 212.5 \]
Since \( F \) must be a whole number, we can round down to 212 (although for the sake of this calculation we can consider \( F \) as either 212 or 213).
Now substituting back to find \( S \):
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If \( F = 212 \): \[ S = 3 \times 212 = 636 \]
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The total number of students would then be \( F + S = 212 + 636 = 848 \).
This is close to 850, so it's a reasonable distribution given the rounding.
Now if rounded \( F = 213 \): \[ S = 3 \times 213 = 639 \]
Again adding gives \( F + S = 213 + 639 = 852 \), which exceeds 850.
Thus we go with \( F = 212 \) and then having:
- Total students taking Spanish: 636.
So the closest and reasonable distribution per the proportions is: \[ S = 636 \]
Therefore, rounding to the nearest whole number: 636 students can choose Spanish.
Final Answers:
- The proportion to use is \( F : S = 1 : 3 \).
- 636 students can take Spanish.
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