In a class of 60 students the number of students who passed biology is 6 more than a number who passed chemistry.Every student passed at least one of the two subjects and 8 students passed both subjects.
I.How many students passed biology?
ii.how many students passed chemistry?
iii.How many students passed only one subject?
To determine the number of students who passed biology, chemistry, and only one subject, we can follow these steps:
Step 1: Start by subtracting the number of students who passed both subjects from the total number of students who passed biology in order to find the number of students who passed biology only.
Step 2: Subtract the number of students who passed both subjects from the total number of students who passed chemistry to find the number of students who passed chemistry only.
Step 3: Finally, add the number of students who passed both subjects to the number of students who passed only one subject, as these students are counted in both the biology and chemistry counts.
Let's solve the problem using these steps:
Given:
Total number of students (class size) = 60
Number of students who passed both biology and chemistry = 8
Number of students who passed biology = Number of students who passed chemistry + 6
I. Determining the number of students who passed biology:
Step 1: Number of students who passed biology only = Number of students who passed biology - Number of students who passed both subjects
Number of students who passed biology only = Number of students who passed biology - 8
Step 2: Number of students who passed biology only = Number of students who passed chemistry + 6 - 8
Number of students who passed biology only = Number of students who passed chemistry - 2
Step 3: Number of students who passed biology = Number of students who passed biology only + Number of students who passed both subjects
Number of students who passed biology = Number of students who passed chemistry - 2 + 8
Number of students who passed biology = Number of students who passed chemistry + 6
Therefore, the number of students who passed biology = Number of students who passed chemistry + 6.
II. Determining the number of students who passed chemistry:
Given that the number of students who passed biology is 6 more than the number who passed chemistry, we can use this information to find the number of students who passed chemistry.
Number of students who passed biology = Number of students who passed chemistry + 6
Since we know the total class size is 60, we can substitute this information into the equation and solve for the number of students who passed chemistry:
60 = Number of students who passed chemistry + Number of students who passed chemistry + 6
Combining like terms:
60 = 2 * Number of students who passed chemistry + 6
Subtract 6 from both sides:
54 = 2 * Number of students who passed chemistry
Divide both sides by 2:
Number of students who passed chemistry = 27
Therefore, the number of students who passed chemistry is 27.
III. Determining the number of students who passed only one subject:
To find the number of students who passed only one subject, we need to subtract the number of students who passed both subjects from the total number of students who passed biology or chemistry.
Number of students who passed only one subject = Total number of students - Number of students who passed both subjects
Number of students who passed only one subject = 60 - 8 = 52
Therefore, the number of students who passed only one subject is 52.