a survey of reading habits of 100 students showed that 30 read both comics and novels. 10 read neither comics nor novels and twice as many students read comics as read novels. 1. illustrate the information on a Venn diagram. 2. how many students read only
so, only 90 read something. That means that if x read novels, then
x + 2x - 30 = 90
Find x, and then you can proceed from there.
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To illustrate the information on a Venn diagram, we need three overlapping circles representing the different groups: students who read comics, students who read novels, and students who read neither.
Let's label the circles:
- C for Comics
- N for Novels
The information provided:
- 30 students read both comics and novels.
- 10 students read neither comics nor novels.
Now let's follow these steps to complete the Venn diagram:
1. Start by placing the 30 students who read both comics and novels in the overlapping area of the C and N circles.
_ _ _ _ _ _ _ _ _ _ _ 30
C| _ _ _ _ _ _ _ _ _ _ _ _
|_ _ _ _ _ _ _ _ _ _ _ _ _
N| _ _ _ _ _ _ _ _ _ _ _
2. The number of students who read only comics can be found by subtracting the 30 students who read both from the total number of students who read comics. It is stated in the question that twice as many students read comics as read novels. Therefore, the number of students who read comics is 2 times the number of students who read novels.
Let's say the number of students who read comics is x and the number of students who read novels is y.
Since x = 2y, we can substitute this value in the diagram:
C| _ _ _ _ _ _ _ _ _ _ _ _ _ _
| _ _ _ _ _ _ _ _ _ _ _ _ _ 30
N| _ _ _ _ _ _ _ _ _ _ _ _ _ _
3. Now, let's find the number of students who read only novels:
Since we know that x = 2y, the number of students who read only comics is 2y - 30.
The number of students who read only novels is y - (2y - 30), which simplifies to 30 - y.
N| _ _ _ _ _ _ _ _ _ _ _ _ _ _
| _ _ _ _ _ _ _ _ _ _ _ _ _ 30-y
C| _ _ _ _ _ _ _ _ _ _ _ _ _ _
| _ _ _ _ _ _ _ _ _ _ _ _ _ 30
4. Finally, we know that there are 10 students who read neither comics nor novels, so we place that number outside the circles:
_ _ _ _ _ _ _ _ _ _ _ 30-y
C| _ _ _ _ _ _ _ _ _ _ _ _ _
| _ _ _ _ _ _ _ _ _ _ _ _ _ 30
N| _ _ _ _ _ _ _ _ _ _ _ _ _ _
Now that the Venn diagram is complete, we can answer the second question:
The number of students who read only novels is represented by the value 30-y. However, without additional information, we cannot determine the exact value of y, thus, we cannot provide the specific number of students who read only novels.