Question

Central highs enrollment decreases at an average rate of 55 students per year, while washington highs enrollment increases at an average rate of 70 students per year. Central high has 2176 students and washington high has 1866 students. If enrollments continue to change at the same rate, when will the two schools have the same number of schools

Answer 1

To find when Central High and Washington High will have the same number of students, set up an equation and solve for x. After approximately 3 years, the two schools will have the same number of students.

Step-by-step explanation:

To find when Central High and Washington High will have the same number of students, we need to set up an equation.

Let x represent the number of years since the current enrollment numbers were recorded.

The current enrollment for Central High is 2176 students, and it decreases at an average rate of 55 students per year. So the equation for Central High's enrollment after x years is: 2176 - 55x

The current enrollment for Washington High is 1866 students, and it increases at an average rate of 70 students per year. So the equation for Washington High's enrollment after x years is: 1866 + 70x

We want to find the value of x when the two equations are equal:

2176 - 55x = 1866 + 70x

Combine like terms:

-55x - 70x = 1866 - 2176

-125x = -310

Divide both sides by -125:

x = -310 / -125

x ≈ 2.48

Since we can't have a fractional number of years, we round up to the next whole year. Therefore, Central High and Washington High will have the same number of students in approximately 3 years.