In this page set word problem4, we will see how to solve the given problem using venn diagram. This problem is little different from the previous problem as one information is missing. Let us take that missing information as x and solve the problem step by step.

Using the same method, student can solve the given practice problem.

When a group of 25 students are surveyed 6 like ice cream, 12 like hot
dogs and 15 like burger. One student said he likes all three. 3 like ice
cream and hot dogs and 3 like ice cream and burger. Assuming that each student like either one of them,

- How many like hot dogs and burger but not ice cream?
- How many like ice cream only?

Solution:

First let us write all the given information.

Number of students like ice cream = 6

Number of students like hot dogs = 12

Number of students like burger = 15

Number of students like all three = 1

Number of students like ice cream and hot dogs = 3

Number of students like ice cream and burger = 3

Here number of students like hot dogs and burger is not given. Let us take that as x. Now let us enter all the given information in the venn diagram.

First let us enter number of students like all three. So we should enter '1' in the area common to three circles. Next we had taken 'x' as number of students like hot dogs and burger. We had already entered 1 in that common area. So students who like only hot dogs and burger but not ice cream is x-1. Similarly number of students like ice cream and hot dogs but not burger is 2(3-1=2) and number of students like ice cream and burger not hot dogs is 2(3-1=2) |

Now let us enter number of students like only burger which is 13-x(15-(2+1+x-1)),number of students like only hot dogs but not ice cream and burger is 10-x(12-(2+1+x-1)) and number of students like only ice cream but not hot dogs and burger is 1(6-(2+2+1)). |

Now we have to solve for x.

Given that the group consists of 25 students. And each student like either one of the given items. Sum of all the entries inside the circle gives the total number of students.

So 25 = 1+2+1+2+10-x+x-1+13-x

25 = 28-x

solving the linear equation we get the value for x.

x = 28-25

x = 3

Answers:

- Number of people like hot dogs and burger but not ice cream

= x-1 = 3-1 = **2**

2. Number of people like ice cream only =** 1**

Practice problem:

A group of 35 people are surveyed. 10 like coffee, 12 like juice and 15 like fresh fruits after breakfast. 3 people like coffee and juice, 5 like juice and fresh fruits. Find how many people like only coffee and fresh fruits but not juice?

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