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 subject and 15 of them like none of the subject then by drawing a veen diagram ,find how many of them (1) like only mathematics (2)like only science
4x-10+x+5x-10+15=95
10x-5=95
10x=95+5
10x=100
x=100รท10
x=10
Assuming you made your Venn diagram, place 10 in the intersection of the two circles.
let the number of students liking Math be 4x and those liking Science be 5x
Then those liking only Math would be 4x-10 , and those liking only Science 5x-10
then
4x-10 + x + 5x-10 + 15 = 95
solve for x, then back-substitute into my definition.
in a group of 95 people the ratio of people who like orange and apple ia 4:5 if 20 of them like bouth the fruits and 5 of them like non of fruits,by drawing a venndaigram find how many them
X=10
Oh, I love math and science! Let's draw a Venn diagram to find out how many students like only math and only science.
1) Let's start by labeling our Venn diagram with the given information.
(MATH)
/ \
/ \
/ \
(10) (x) (15)
/ \
/ \
/ \
(1) (2)
(SCIENCE)
So, we know that there are a total of 95 students in the group, and we also know that 15 students like neither math nor science. Let's call the number of students who like only math "x", and the number who like only science "y".
Now, we can use the given ratio to set up an equation.
The ratio of students who like math and science is 4:5, so the number of students who like both is (5/9) * (95 - 15 - x - y) = 10.
Simplifying the equation, we have:
(5/9) * (80 - x - y) = 10
Now we can solve for x and y. I'll leave the math to you!
To solve this problem, we can use a Venn diagram to visually represent the given information.
Step 1: Draw two intersecting circles to represent mathematics (M) and science (S).
Step 2: Label the region where the circles intersect as "Both" since this represents the students who like both subjects.
Step 3: Since we know the ratio of students who like mathematics and science is 4:5, we can divide the 95 students into 9 equal parts (4 parts for mathematics and 5 parts for science). Draw four sections outside the intersection in the mathematics circle and five sections outside the intersection in the science circle.
Step 4: Label the remaining sections in the mathematics circle as "Mathematics Only" to represent the students who like only mathematics. Similarly, label the remaining sections in the science circle as "Science Only" to represent the students who like only science.
Now, let's calculate the number of students who like only mathematics and those who like only science.
Step 5: Start by filling in the information we already know. In the intersection, write down that 10 students like both subjects. In the outer sections of the mathematics circle, write down the number of students who like only mathematics. Similarly, do the same for the science circle.
Step 6: Given that 15 students like none of the subjects, place this number outside the circles.
Step 7: Since the total number of students is 95, we can add up the numbers in the Venn diagram to find the remaining sections.
Step 8: Once you have filled in all the information, count the number of students in the "Mathematics Only" section to find the answer to (1) and count the number of students in the "Science Only" section to find the answer to (2).
That's it! By following these steps and using the given ratio and data, you can determine the number of students who like only mathematics and only science.