Out of four hundred students in the final year in a Senior high school,300 are offering biology and 190 are offering chemistry.
(1) How many students offering both subject,if 70 students offering neither biology nor chemistry?
(3) How many students offering chemistry only?
To find out how many students are offering both biology and chemistry, we can use the principle of inclusion-exclusion.
Let's break it down step by step:
Step 1: Start with the total number of students in the final year, which is 400.
Step 2: Subtract the number of students offering neither biology nor chemistry, which is 70. This gives us 400 - 70 = 330 students who are offering either biology or chemistry or both.
Step 3: Subtract the number of students offering biology. Since 300 students are offering biology, we subtract 300 from the previous result: 330 - 300 = 30 students offering only chemistry.
Therefore, 30 students are offering chemistry only.
Please note that we haven't calculated the number of students offering both subjects yet. To find that, we need to determine the number of students offering only biology.
(2) How many students are offering biology only?
Step 1: Start with the total number of students offering biology (300).
Step 2: Subtract the number of students offering both biology and chemistry. This gives us 300 - x, where x represents the number of students offering both subjects.
Step 3: Subtract the number of students offering neither biology nor chemistry (70). This gives us 300 - x - 70.
Since the remaining students (300 - x - 70) are offering only biology, we can say that (300 - x - 70) = x.
Simplifying this equation, we get:
300 - 70 = 2x
230 = 2x
x = 115
Therefore, 115 students are offering both biology and chemistry.
In summary:
- The number of students offering both biology and chemistry is 115.
- The number of students offering chemistry only is 30.