To determine the proportion of students choosing Spanish and French, we first need to establish the ratio of Spanish classes to French classes. We have been told that there are 3 times as many Spanish classes as French classes, which gives us a ratio of Spanish to French classes as 3:1.
Let's denote:
- the number of French classes as \( F \)
- the number of Spanish classes as \( S \)
From the information given, we have: \[ S = 3F \]
The total number of classes of both languages is then: \[ F + S = F + 3F = 4F \]
Next, we need to find the proportion of students that can choose Spanish. The total number of students is 850. The proportion of students taking Spanish is represented by the ratio of Spanish classes to the total number of classes:
\[ \text{Proportion of students in Spanish} = \frac{S}{F + S} = \frac{3F}{4F} = \frac{3}{4} \]
Now, we can calculate how many students choose Spanish by using this proportion: \[ \text{Number of students choosing Spanish} = 850 \times \frac{3}{4} \]
Calculating that: \[ 850 \times \frac{3}{4} = 850 \times 0.75 = 637.5 \]
Rounding to the nearest whole number, we get 638 students.
Responses:
- 638 students can take Spanish.