In a class of 60students, if the number of students who offer Maths is twice the number of students who offer English if 9 students offer both subjects and 3 students offer none of the subject, find the number of students who offer (i) maths
(ii) English
(iii) maths only
(iv) English only
57 (60 - 3) are M, E, or ME
... E + M + ME = 57
... E + M = 48
M + ME = 2 (E + ME)
... M + 9 = 2E + 18 ... M = 2E + 9
substituting
... E + 2E + 9 = 48 ... E = 13
(i) M + ME
(ii) E + ME
(iii) M
(iv) E
6
7
9
8
To solve this problem, let's break it down step by step.
Step 1: Define the given information
In a class of 60 students,
- The number of students who offer Maths is twice the number of students who offer English.
- 9 students offer both Maths and English.
- 3 students offer none of the subjects.
Step 2: Represent the given information
Let's use the following variables:
- Let "M" represent the number of students who offer Maths.
- Let "E" represent the number of students who offer English.
- Let's represent the number of students who offer both Maths and English as "B" (for "both").
- Let's represent the number of students who offer neither Maths nor English as "N" (for "none").
So now we have:
M + E = 60 (since the total number of students is 60)
M = 2E (since the number of students who offer Maths is twice the number of students who offer English)
B = 9 (the number of students who offer both Maths and English)
N = 3 (the number of students who offer neither Maths nor English)
Step 3: Solve for the unknowns
We can solve this system of equations using substitution or elimination.
From the equation M = 2E, we can substitute this value into the equation M + E = 60:
2E + E = 60
3E = 60
E = 20
Substituting this value back into M = 2E:
M = 2 * 20
M = 40
Step 4: Find the number of students who offer Maths only and English only
To find the number of students who offer Maths only, we subtract the number of students who offer both Maths and English (B) from the total number of students who offer Maths (M):
Maths only = M - B = 40 - 9 = 31
Similarly, to find the number of students who offer English only, we subtract the number of students who offer both Maths and English (B) from the total number of students who offer English (E):
English only = E - B = 20 - 9 = 11
Step 5: Summarize the results
(i) The number of students who offer Maths: M = 40
(ii) The number of students who offer English: E = 20
(iii) The number of students who offer Maths only: Maths only = 31
(iv) The number of students who offer English only: English only = 11