Question

The student-teacher ratio in a school is 45:2. If there are 4050 students in the school how many teachers must be there?

Answer 1

Hint: First, assume the number of teachers in the school. Then, use the formula of the ratio to find the total number of the teachers in the school which is the total number of students in the school divided by the total number of the teachers in the school.

Complete step-by-step answer:
Given:- Ratio of the students to the teachers in a school is 45:2.
The total number of students in a school is 4050.
Let assume the total number of the teacher in a school be x.
The ratio is defined as the quantity of one thing concerning the other thing in simplified form. It can be represented in many ways by using the symbols: / or as a decimal or as a percentage.
The formula of the ratio is,
Ratio= $\dfrac{a}{b}$
Put a= total number of the students in a school and b= total number of teachers in that school and the value of the ratio is \[\dfrac{{45}}{2}\]. Then,
$\dfrac{{45}}{2} = \dfrac{{4050}}{x}$
Now, cross multiply the terms of the equation,
$45x = 8100$
Now, divide both sides by 45 of the equation,
$\dfrac{{45x}}{{45}} = \dfrac{{8100}}{{45}}$
Cancel out the common factor on both sides,
$x = 180$

Hence, the total number of the teachers in a school are 180.

Note: A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent. The ratio is denoted by :