Representatives from the student councils at three area high schools are traveling to the national convention in New York. North Springdale High School is sending 5 more students than South Springdale High School and West Springdale High School is sending 6 more students than North Springdale. The three schools are sending a total of 46 students to the convention. How many of the students are coming from North Springdale?

Responses

A 10 students10 students

B 15 students15 students

C 21 students21 students

D 30 students30

1 answer

Let the number of students from South Springdale High School be represented as \( x \).

According to the problem:

The total number of students from all three schools can be represented by the equation:

\[ x + (x + 5) + (x + 11) = 46 \]

Now, we can simplify this equation:

\[ x + x + 5 + x + 11 = 46 \] \[ 3x + 16 = 46 \]

Next, we will solve for \( x \):

\[ 3x = 46 - 16 \] \[ 3x = 30 \] \[ x = 10 \]

Now that we have \( x \), we can determine the number of students from North Springdale High School:

\[ \text{Students from North Springdale} = x + 5 = 10 + 5 = 15 \]

Thus, the number of students coming from North Springdale is:

\[ \boxed{15} \]