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?

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

GPT-4o mini · Answer

Let $ x $ be the number of students from South Springdale High School. 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. The total number of students sent by all three schools can therefore be expressed as: $$ x + (x + 5) + (x + 11) = 46 $$ Simplifying this equation: $$ x + x + 5 + x + 11 = 46 $$ $$ 3x + 16 = 46 $$ Now, subtract 16 from both sides: $$ 3x = 46 - 16 $$ $$ 3x = 30 $$ Now divide by 3: $$ x = 10 $$ Now that we have the number of students from South Springdale High School, we can find the number of students from North Springdale High School: $$ \text{North Springdale} = x + 5 = 10 + 5 = 15 $$ Thus, the number of students coming from North Springdale High School is $ \boxed{15} $.