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AQA GCSE · Question 07.1 · Ratio Proportion and Rates of Change
At a school there are 912 students. The ratio of students to teachers is 15.2 : 1. The number of students stays the same. The number of teachers increases by 2. Work out the new ratio of students to teachers. Give your answer in the form n : 1.
At a school there are 912 students. The ratio of students to teachers is 15.2 : 1. The number of students stays the same. The number of teachers increases by 2. Work out the new ratio of students to teachers. Give your answer in the form n : 1.
How to approach this question
1. Use the initial ratio and the number of students to calculate the original number of teachers.
2. Calculate the new number of teachers after the increase.
3. Write down the new ratio of students to teachers using the new number of teachers.
4. Simplify this new ratio so that it is in the form n : 1 by dividing the number of students by the new number of teachers.
Full Answer
1. Find the original number of teachers.
The ratio is students : teachers = 15.2 : 1.
Number of teachers = Total students / 15.2
Number of teachers = 912 / 15.2 = 60.
2. Find the new number of teachers.
The number of teachers increases by 2.
New number of teachers = 60 + 2 = 62.
3. Work out the new ratio.
The number of students is still 912.
New ratio = students : new teachers = 912 : 62.
4. Simplify the ratio to the form n : 1.
To get the right side to be 1, we divide both sides by 62.
n = 912 / 62 ≈ 14.7096...
So the new ratio is 14.7 : 1 (to 3 s.f.).
Step 1: Find the original number of teachers.
The ratio of students to teachers is 15.2 : 1. This means for every teacher, there are 15.2 students.
To find the number of teachers, we can divide the total number of students by 15.2.
Original number of teachers = 912 ÷ 15.2 = 60.
Step 2: Find the new number of teachers.
The number of teachers increases by 2.
New number of teachers = 60 + 2 = 62.
Step 3: Write the new ratio.
The number of students remains 912. The new number of teachers is 62.
The new ratio is 912 : 62.
Step 4: Simplify the ratio to the form n : 1.
To make the right-hand side of the ratio equal to 1, we need to divide both parts of the ratio by 62.
(912 ÷ 62) : (62 ÷ 62)
14.7096... : 1
Rounding to one decimal place, the ratio is 14.7 : 1.
Common mistakes
✗ Multiplying 912 by 15.2 instead of dividing.
✗ Incorrectly calculating the new number of teachers.
✗ Leaving the answer as 912 : 62 instead of simplifying to the required form n : 1.
✗ Dividing 62 by 912 instead of the other way around when simplifying.
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