The incoming 7th grade class has a choice of french or spanish as a language elective. There are 3 times as many Spanish classes as french classes (or 3 to 1). How many students can choose spanish if there are 850 students? Round to the nearest whole number. (1 point)
First, we need to find the total number of classes. Let's call the number of French classes F and the number of Spanish classes S.
We know that S = 3F.
From this information, we can create an equation: F + S = total number of classes.
Using the substitution method, we substitute 3F in place of S in the equation: F + 3F = total number of classes.
Combining like terms, we have 4F = total number of classes.
Dividing both sides of the equation by 4, we find that F = (total number of classes)/4.
Since the total number of students is 850, and each class has an equal number of students, we have F + S = total number of classes = 850/number of students per class.
Therefore, F + 3F = 850/number of students per class.
Combining like terms, we get 4F = 850/number of students per class.
Dividing both sides of the equation by 4, we find that F = (850/number of students per class)/4.
Since we want to round to the nearest whole number, we need to determine the number of students per class.
To do this, we divide the total number of students by the total number of classes: number of students per class = 850/number of classes.
Substituting the value of F we found earlier, we have number of students per class = 850/(850/number of students per class)/4.
Simplifying, we have number of students per class = 850 * 4 / 850 = 4.
Therefore, there are 4 students in each class.
Substituting this value into the equation F + 3F = 850/number of students per class, we have F + 3F = 850 / 4.
Combining like terms, we get 4F = 850/4.
Dividing both sides of the equation by 4, we find that F = 850/4.
Rounding to the nearest whole number, we find that F = 213.
Since S = 3F, we have S = 3 * 213 = 639.
Therefore, approximately 639 students can choose Spanish as their language elective.