To determine the proportion of students that can choose Spanish, we begin by defining variables for the number of French and Spanish classes.
Let:
- \( F \) = number of French classes
- \( S \) = number of Spanish classes
According to the problem, we have the relationship: \[ S = 3F \] This means there are three times as many Spanish classes as French classes.
Now, let's denote the number of students who choose French and Spanish. We can consider that each class can accommodate the same number of students. Let's assume each class has \( x \) students. Therefore, the total number of students choosing French would be \( F \times x \) and those choosing Spanish would be \( S \times x \).
Since \( S = 3F \), the number of students choosing Spanish can be expressed as: \[ S \times x = 3F \times x = 3(F \times x) \]
Now, let’s denote the total number of students: \[ F \times x + S \times x = 850 \]
Substituting \( S = 3F \): \[ F \times x + 3F \times x = 850 \] \[ 4F \times x = 850 \]
Now we can express the number of students choosing Spanish: \[ S \times x = 3F \times x = \frac{3}{4} \times 850 \]
To find this value: \[ \text{Number of students choosing Spanish} = \frac{3}{4} \times 850 = 637.5 \]
Since the number of students must be a whole number, and this calculation intends to show the division evenly, we can adjust the proportion correctly as follows:
The proportion we are looking for to determine the number of students that can choose Spanish is: \[ \frac{\text{Number of Spanish classes}}{\text{Total number of classes}} \]
Total classes = \( F + S = F + 3F = 4F \).
Thus, the ratio of Spanish classes to total classes is: \[ \frac{S}{F + S} = \frac{3F}{4F} = \frac{3}{4} \]
Therefore, the proportion to use to solve this problem is \( \frac{3}{4} \).