Make your Venn diagram of two overlapping circles.
Place 5 in the intersection of the circles, (5 take both subjects)
number taking Economics = e
number taking Accounting = 2e
(2e - 5) + 5 + (e - 5) + 10 = 50
3e = 45
e = 15
those taking only 1 subject = 2e-5 + e-5
= 35
Your Venn diagram should match my answers
In a class of 50 students,the number of students who offer Accounting is twice as the number who offer Economics.10 students offer neither of the two subjects and 5 students offer both subjects.Illustrate this information on the Venn diagram.How many students offer Economics.How many students offer only one subject?
10 answers
You replace 5 in the intersection
No solve into deteil
I want Clear one
Show diagram
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In a class of 50 students, the number of students who offer accounting is twice as the number who offer economics.10 students offer neither of the two subjects and 5 students offer both subjects.
Based on this information, we can make the following Venn diagram:
```
_______________
/ \
/ \
_____/___E______A___\
| \
| 5 \
|___________________/
| |
| |
| |
/ \
/ \
/________________\
| |
| |
| |
10 x
```
In this diagram, E represents the students who offer economics, A represents the students who offer accounting, and x represents the number of students who offer both subjects (which we know is 5). The total number of students is 50, so we know that the sum of all the regions in the diagram must be 50.
We also know that the number of students who offer accounting is twice the number who offer economics. So, we can use algebra to solve for the number of students in each region of the diagram:
- Let e be the number of students who offer economics
- Then, the number of students who offer accounting is 2e
- The number of students who offer neither subject is 10
- The number of students who offer both subjects is 5
Using this information, we can set up the following equation:
```
e + 2e + 10 + 5 = 50
3e + 15 = 50
3e = 35
e = 12
```
So, there are 12 students who offer economics and 2e = 24 students who offer accounting. The number of students who offer only one subject is:
```
(12 - 5) + (24 - 5) = 6 + 19 = 25
```
Therefore, 12 students offer economics, 24 students offer accounting, and 25 students offer only one subject.
```
_______________
/ \
/ \
_____/___E______A___\
| \
| 5 \
|___________________/
| |
| |
| |
/ \
/ \
/________________\
| |
| |
| |
10 x
```
In this diagram, E represents the students who offer economics, A represents the students who offer accounting, and x represents the number of students who offer both subjects (which we know is 5). The total number of students is 50, so we know that the sum of all the regions in the diagram must be 50.
We also know that the number of students who offer accounting is twice the number who offer economics. So, we can use algebra to solve for the number of students in each region of the diagram:
- Let e be the number of students who offer economics
- Then, the number of students who offer accounting is 2e
- The number of students who offer neither subject is 10
- The number of students who offer both subjects is 5
Using this information, we can set up the following equation:
```
e + 2e + 10 + 5 = 50
3e + 15 = 50
3e = 35
e = 12
```
So, there are 12 students who offer economics and 2e = 24 students who offer accounting. The number of students who offer only one subject is:
```
(12 - 5) + (24 - 5) = 6 + 19 = 25
```
Therefore, 12 students offer economics, 24 students offer accounting, and 25 students offer only one subject.
27 answers