Ask a New Question
Menu

In a class of 38 student each leading study at least one of the following subjects French mathematics and history the following table give further details of the subject studies French only 9 mathematics eight history only one French and mathematics 7 French and history 8

1 answer

To analyze the distribution of students studying French, Mathematics, and History in your class, we can summarize the information provided and find how many students study each combination of subjects.

Let's break it down:

  1. Students studying only French: 9
  2. Students studying only Mathematics: 8
  3. Students studying only History: 1
  4. Students studying both French and Mathematics: 7
  5. Students studying both French and History: 8
  6. Students studying both Mathematics and History: (not provided)
  7. Students studying all three subjects: (not provided)

To get the total number of students enrolled, we need to find out how many students might be studying all three subjects and those who study Mathematics and History only.

Let’s use a Venn Diagram approach to get the complete picture of the subjects.

Let:

  • \( x \) = Number of students studying all three subjects (French, Mathematics, and History).
  • \( y \) = Students studying both Mathematics and History only.

Using the information:

From the combinations we have:

  1. Students studying only French = 9
  2. Students studying only Mathematics = 8
  3. Students studying only History = 1
  4. Students studying French and Mathematics but not History = 7 - \( x \)
  5. Students studying French and History but not Mathematics = 8 - \( x \)
  6. Students studying Mathematics and History but not French = \( y \)

Equations:

Now, we know that the sum of all these categories should equal the total number of students (38):

\[ 9 + 8 + 1 + (7 - x) + (8 - x) + y + x = 38 \]

This simplifies to:

\[ 9 + 8 + 1 + 7 + 8 + y + (7 - 2x) = 38 \] \[ 33 + y - 2x = 38 \] \[ y - 2x = 5 \tag{1} \]

We also know that:

The number of students taking just Mathematics and History can be derived from:

From earlier, we noted the counts of students involved in various groups. To fully dive deeper, for \(y\):

  • Since \( y = (Math and History) - x \), we can also express it as \( y = m + x \). Summarily we will need more information about the specific groups.

Final Assumptions:

  • \( x \) cannot exceed the total of any of the groups (e.g., must not exceed pairs).

To solve for \( x \), we can either try different logical values or create scenarios where exact counts align with certain output counts.

If you have additional data, or calculated outcomes or specific values for \(x\) or \(y\) those will be essential to produce complete counts.

Could you provide any further information?