Question

There are 30 students in the class. 15 study woodwork and 13 study metalwork. 6 study neither of the two subjects. How many study woodwork but not metalwork ​

Answer 1

To find the number of students who study woodwork but not metalwork, subtract the number of students who study both subjects from the total number of students who study woodwork.

Step-by-step explanation:

To find the number of students who study woodwork but not metalwork, we need to subtract the number of students who study both woodwork and metalwork from the total number of students who study woodwork.

We are given that there are 30 students in total, 15 study woodwork, and 13 study metalwork. 6 students study neither subjects.

So, the number of students who study woodwork but not metalwork is:

Number of students studying woodwork - Number of students studying both woodwork and metalwork

= 15 - (Total number of students - Number of students studying neither subjects)

= 15 - (30 - 6)

= 15 - 24

= 9

Answer 2

11 students study woodwork but not metalwork

Step-by-step explanation:

Since there are 30 students in total and 6 study neither woodwork nor metalwork, there are 30 - 6 = 24 students who study at least one of the two subjects.

Since 15 students study woodwork and 13 study metalwork, there are 15 + 13 = 28 students who study woodwork or metalwork or both.

Subtracting the number of students who study at least one of the two subjects from the number of students who study woodwork or metalwork or both, we get 28 - 24 = 4 students who study both woodwork and metalwork.

Therefore, the number of students who study woodwork but not metalwork is 15 - 4 = 11

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Step 1: Determine the number of students who study at least one of the two subjects:

Since there are:

• 30 students altogether,
• and 6 study neither woodwork nor metalwork,

we can determine the number of students who study at least one of the two subjects by subtracting 6 from 30:

30 - 6

24

Thus, 24 students study at least one of the two subjects.

Step 2: Determine the number of students who study either woodwork or metalwork or both:

Since:

• 15 students study woodwork,
• and 13 study metalwork,

we can determine the number of students who study either woodwork or metalwork or both by adding 15 and 13:

15 + 13

28

Thus, 28 students either woodwork or metalwork or both.

Step 3: Determine the number of students who study both subjects:

We can determine the number of students who study both subjects by:

• subtracting the number of students who study at least one of the two subjects (24) from the number of students who study woodwork or metalwork or both (28):

28 - 24

4

Thus, 4 students study both subjects.

Step 4: Determine the number of students who study woodwork but not metal work

Now we can find the number of students who study woodwork by:

• subtracting the number of students who study both subjects (4) from the total number of students who study woodwork (15):

15 - 4

11

Thus, 11 students study woodwork but not metalwork.