Question

Cristine's middle school has a total of 900 students and 45 teachers. The local high school has 110 teachers and a student-teacher ratio proportional to the middle school's. How many students will Cristine find when she gets to high school? A) 900 B) 1100 C) 2200 D) 2500

Answer 1

Write and solve an equation of ratios:

900 students 45 teachers
------------------ = -----------------
x 110 teachers

Cross multiplying, we get (900)(110) / 45, or


so x = # of students in the high school = 2200 (answer)

Answer 2

Option C. 2200 is correct

Explanation:

Number of teachers in middle school = 45

Number of students in middle school = 900

`\text{Ratio of students to teacher in middle school = }(900)/(45)`

Number of teachers in Local high school = 110

Let number of students in local high school = x

`\text{Ratio of students to teacher in local high school = }(x)/(110)`

But, according too the question, both the ratios are given proportional to each other.

⇒ Ratio of students to teacher in middle school = Ratio of students to teacher in local high school

`\implies (900)/(45)=(x)/(110)\\\\\implies x=(110* 900)/(45)\\\\\implies x = 2200`

Hence, number of students required in the local high school = 2200

Therefore, Option C. 2200 is correct