In a group of 95 students , the ratio of students who like mathematics and science is 4:5 . if 10 of them like both the subjects and 15 of them like none of the subjects then by drawing a venn diagram,find how many of them like only mathematics and how many of them only likescience
Place 10 in the intersection.
Put 4x - 10 in the "math only" field
Put 5x - 10 in the "science only" field
then 4x-10 + 5x-10 + 10 + 15 = 95
9x = 90
x = 10
Place 10 in the intersection.
Put 4x - 10 in the "math only" field
Put 5x - 10 in the "science only" field
then 4x-10 + 5x-10 + 10 + 15 = 95
9x = 90
x = 10
and acc to question
4x= 4 * 10 = 40
3x= 3 * 10 = 30
Why did the math book go to the therapist?
Because it had too many problems!
Now, let's solve this problem using a Venn diagram!
Let's represent the students who like mathematics and science as "M" and "S", respectively.
According to the information given, the ratio of students who like mathematics and science is 4:5. So, we'll divide the overlapping region into two parts, one representing only mathematics (M) and the other representing only science (S).
We are also given that 10 students like both subjects and 15 students like none. Let's fill in those numbers on our diagram.
M
_
| | _
S | | | |
|_|___|_|
Now, let's do some calculations.
The total number of students who like mathematics and science is 4x + 5x = 9x, where x is a constant.
The total number of students who like only mathematics is 4x - 10 (subtracting the 10 students who like both from the mathematics total).
The total number of students who like only science is 5x - 10 (subtracting the 10 students who like both from the science total).
We are also given that 15 students like none. So, we need to subtract this from the total number of students.
Therefore, the number of students who like only mathematics is (4x - 10) - 15 = 4x - 25 ,
and the number of students who like only science is (5x - 10) - 15 = 5x - 25.
Unfortunately, without knowing the value of x, we can't determine the exact number of students who like only mathematics or science. We can only express them in terms of x, leaving as an algebraic expression.
To find out how many students like only mathematics and how many students like only science, we can start by drawing a Venn diagram.
1. Begin by drawing two intersecting circles, representing mathematics and science.
2. Label one circle as "Mathematics" and the other as "Science."
3. Inside the intersection of the two circles, write the number of students who like both mathematics and science, which is 10.
4. Outside the intersection of the circles, label one area as "Only Mathematics" and the other area as "Only Science."
Now, we need to determine the number of students in each of these areas.
To do so, we need to use the information given in the problem - the ratio of students who like mathematics and science is 4:5, and the total number of students is 95.
First, we can set up a proportion to find the number of students who like mathematics:
4 (students who like math) / (4 + 5) (total parts) = Number of students who like math / 95 (total number of students)
Simplifying the proportion:
4 / 9 = Number of students who like math / 95
Cross-multiplying and solving for the number of students who like math:
Number of students who like math = (4 / 9) * 95
Next, we can find the number of students who like science:
5 (students who like science) / (4 + 5) (total parts) = Number of students who like science / 95 (total number of students)
Simplifying the proportion:
5 / 9 = Number of students who like science / 95
Cross-multiplying and solving for the number of students who like science:
Number of students who like science = (5 / 9) * 95
Finally, we subtract the number of students who like both math and science from the totals we just calculated:
Number of students who like only math = Number of students who like math - Number of students who like both math and science
Number of students who like only science = Number of students who like science - Number of students who like both math and science
By substituting the values, you will get the exact number of students who like only mathematics and only science.
Place 10 in the intersection.
Put 4x - 10 in the "math only" field
Put 5x - 10 in the "science only" field
then 4x-10 + 5x-10 + 10 + 15 = 95
9x = 90
x = 10
and acc to question
4x= 4 * 10 = 40
3x= 3 * 10 = 30
fill in all the fields of your Venn diagram.
Place 10 in the intersection.
Put 4x - 10 in the "math only" field
Put 5x - 10 in the "science only" field
then 4x-10 + 5x-10 + 10 + 15 = 95
9x = 90
x = 9
Now you know each of the entries in the Venn diagram.