Question

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 \( x \).

According to the problem:

North Springdale High School is sending \( x + 5 \) students.
West Springdale High School is sending \( (x + 5) + 6 = x + 11 \) students.

Now we can express the total number of students sent by all three schools as:

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

Combining like terms:

\[ 3x + 16 = 46 \]

Now, we can isolate \( x \):

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

Now we know:

South Springdale High School sends \( x = 10 \) students.
North Springdale High School sends \( x + 5 = 10 + 5 = 15 \) students.
West Springdale High School sends \( x + 11 = 10 + 11 = 21 \) students.

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

\[ \boxed{15} \]

This corresponds to option B: 15 students.