Question

Each of the 56 pupils in the fourth year of a small school studies one of the subjects History, English and Agriculture. Of the 14 pupils who study agriculture, 4 also study History and English, 3 study neither History nor English and 5 study English but not History Of the 42 pupils who do not study Agriculture, 6 study both History and English x study only History and 2x study only English. Find the value of x,

Answer 1

By creating a Venn diagram to organize the provided information, solving the resulting equation shows that the value of x (the number of pupils who study only History and not Agriculture) is 12.

Step-by-step explanation:

The student's question involves a problem of counting and probability, which falls under the subject of Mathematics, more specifically a high school level combinatorics problem. Given the number of students and the breakdown of how many study each combination of subjects, we can use a Venn diagram to visualize and solve for the unknown variable x. Let's break down the information:

• There are 56 pupils in total.
• 14 pupils study Agriculture: 4 study both History and English, 3 study neither History nor English, and 5 study English but not History.
• 42 pupils do not study Agriculture: of these, 6 study both History and English, x study only History, and 2x study only English.

Adding the numbers up, we have the total number of pupils that do not study Agriculture:

6 + x + 2x = 42

Simplifying, we get:

3x + 6 = 42

Subtract 6 from both sides:

3x = 36

Divide both sides by 3:

x = 12

Therefore, the value of x representing the number of pupils who study only History but not Agriculture is 12.

Answer 2

To find the value of x, we need to use the given information to set up equations and solve for x.

Step-by-step explanation:

To find the value of x, let's break down the information given.

There are 56 pupils in total. Out of these, 14 study Agriculture, 5 study only English, and 4 study both History and English. This means that there are 14 - 4 = 10 pupils who study only Agriculture.

So, out of the 56 pupils, 10 study only Agriculture, and 4 study both History and English. This leaves us with 56 - 14 = 42 pupils who study neither History nor English. But we are given that 3 study neither History nor English, so we subtract these 3 from the total.

Therefore, the number of pupils who study History and English is 42 - 3 = 39.

Now, let's consider the 42 pupils who do not study Agriculture. It is given that 6 of them study both History and English and x study only History. This means that 42 - 6 - x = 36 - x study only English.

But we are also given that 2x study only English. So, we can write the equation 36 - x = 2x. Solving this equation, we get x = 12.