In the first year of a school, there were 116 student who took mathematics and science.they all passed at least one subject and 34 passed both subject.if twice as many as science as passed mathematic, find how many passed in mathematics only
To find the number of students who passed only in mathematics, we need to subtract the number of students who passed both mathematics and science from the total number of students who passed mathematics.
Let's break down the given information:
- Total number of students who took mathematics and science = 116
- Number of students who passed both subjects = 34
- Number of students who passed at least one subject = Total number of students who took mathematics and science - Number of students who passed neither subject
To determine the number of students who passed neither subject, we can use the principle of inclusion-exclusion. The principle states that the number of students who passed at least one subject equals the sum of the number of students who passed mathematics only, the number of students who passed science only, and the number of students who passed both subjects, minus the number of students who passed neither subject.
Let's denote:
- Number of students who passed mathematics only = x
- Number of students who passed science only = y
- Number of students who passed neither subject = z
According to the given information:
116 = x + y + 34 - z
We also know that "twice as many as science as passed mathematics," which means the number of students who passed science only (y) is double the number of students who passed mathematics only (x).
y = 2x
Now, let's substitute the value of y in terms of x into the equation:
116 = x + 2x + 34 - z
Simplifying the equation:
116 = 3x + 34 - z
Now, we need to isolate the x term:
3x = 116 - 34 + z
3x = 82 + z
To find the number of students who passed only in mathematics (x), we need more information about the number of students who passed neither subject (z). Without that information, we cannot determine the exact value of x.