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In a school, $ rac{2}{3}$ of the students study a language - OCR - GCSE Maths - Question 4 - 2017 - Paper 1
Question 4
In a school, $ rac{2}{3}$ of the students study a language. Of those students who study a language, $ rac{2}{5}$ study Spanish. Find the ratio of students who stud... show full transcript
Worked Solution & Example Answer:In a school, $ rac{2}{3}$ of the students study a language - OCR - GCSE Maths - Question 4 - 2017 - Paper 1
Step 1
Of those students who study a language, $ rac{2}{5}$ study Spanish
Answer
Let the total number of students be represented as .
The number of students studying a language is given by: ext{Students studying a language} = rac{2}{3} n.
Then, the number of students studying Spanish is: ext{Students studying Spanish} = rac{2}{5} imes rac{2}{3} n = rac{4}{15} n.
Step 2
Find the students who do not study Spanish
Answer
To find the students who do not study Spanish, we first calculate those who study a language but do not study Spanish:
The students studying a language are rac{2}{3} n, and the students studying Spanish are rac{4}{15} n.
Thus, the students who do not study Spanish are: ext{Students not studying Spanish} = rac{2}{3} n - rac{4}{15} n.
Finding a common denominator (which is 15): rac{2}{3} n = rac{10}{15} n.
So, ext{Students not studying Spanish} = rac{10}{15} n - rac{4}{15} n = rac{6}{15} n = rac{2}{5} n.
Step 3
Calculate the ratio of students who study Spanish to those who do not
Answer
The ratio of students who study Spanish to those who do not study Spanish is given by: ext{Ratio} = rac{ ext{Students studying Spanish}}{ ext{Students not studying Spanish}} = rac{ rac{4}{15} n}{ rac{2}{5} n}.
This simplifies to: ext{Ratio} = rac{4/15}{2/5} = rac{4}{15} imes rac{5}{2} = rac{20}{30} = rac{2}{3}.
Thus, the final ratio, in its simplest form, is: