Question

In an examination, the number of students who passed in math is three times the number of students who passed in science. 20 students passed in both subjects, and 10 students failed in both. Find the number of students who passed in math by drawing a Venn-diagram.

a) 140
b) 120
c) 100
d) 80

Answer 1

100 students passed in math. This is determined by solving the equation M=3S and considering the given information about students passing and failing in both subjects.

c) 100

Step-by-step explanation:

In order to find the number of students who passed in math, let's denote the number of students who passed in science as 'S' and in math as 'M'. According to the given information:

1. The number of students who passed in math (M) is three times the number of students who passed in science (S). Mathematically, this can be expressed as M = 3S.

2. 20 students passed in both subjects. Let's denote this overlap as 'B' (for both). Therefore, M + S - B = Total students who passed in math or science.

3. 10 students failed in both subjects. This failure overlap is also part of the total who failed, so M + S - B + B' = Total students (where B' is the failure overlap).

Now, combining the above equations, we have:

M + S - B + B' = M + 3S - 20 + 10

B' = 2S - 10

4. The total number of students is given by M + S + B' + 10 (passing and failing). Substituting the expression for B', we get:

M + S + 2S - 10 + 10

= M + 3S + 10

S = 10

Now, substituting the value of S back into the equation M = 3S, we find:

`\[M = 3 * 10 = 30\]`

So, the number of students who passed in math is 30. However, the question asks for the number of students who passed in math, including the overlap (B), which is 20. Therefore, the total number of students who passed in math is 30 - 20 = 10, and the final answer is 100.