Question

A small town has two local high schools. High School A currently has 800 students and is projected to grow by 55 students each year. High School B currently has 950 students and is projected to grow by 25 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine the interval of years, t,t, for which High School A will have more students than High School B.

Answer 1

To write an equation for each situation, we need to determine the number of students in High School A and in High School B after a certain number of years. The equations for High School A and High School B can be written as AA = 800 + 55t and BB = 950 + 25t. The interval of years for which High School A will have more students than High School B is t > 5.

Step-by-step explanation:

To write an equation for each situation, we need to determine the number of students in High School A (AA) and in High School B (BB) after a certain number of years (tt). We can use the given information to write the following equations:

AA = 800 + 55t

BB = 950 + 25t

To find the interval of years for which High School A will have more students than High School B, we need to solve the inequality AA > BB:

800 + 55t > 950 + 25t

30t > 150

t > 5

The interval of years for which High School A will have more students than High School B is t > 5.