In a survey of 50 students, 23 owned cellular phones, 18 ownded digital cameras, X owned cellular phones and digital camera, 2X owned neither.
a) How do i write an expression in X for the Total number of students in the survey and how do i find for X????
23-X owned digital camers ONLY
18-X owned a cell phone ONLY
X owned both
2X owned neither.
Those are the only four possibilities, so the sum must equal 50.
41 - 2X +X +2X = 50
41 +X = 50
X = 9
how to represent this in a venn diagram
in a survey of 50 students , 23 owned cellular phones, 18 owned digital cameras, x owned cellular phones and digital cameras,2x owned neither
To write an expression in terms of X for the total number of students in the survey, you can consider the different groups of students.
Let's define:
A = number of students who own cellular phones
B = number of students who own digital cameras
C = number of students who own both cellular phones and digital cameras
D = number of students who own neither cellular phones nor digital cameras
According to the information given:
A = 23 (students who own cellular phones)
B = 18 (students who own digital cameras)
C = X (students who own both cellular phones and digital cameras)
D = 2X (students who own neither)
The total number of students is the sum of these groups:
Total number of students = A + B + D
Substituting the given values:
Total number of students = 23 + 18 + 2X
To find the value of X, you need to solve the equation. However, the information provided in the statement is not sufficient to determine the value of X.
To write an expression for the total number of students in the survey, you can make use of the principle of inclusion-exclusion, which states that the total number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements in their intersection.
Let's analyze the given information:
- 23 students owned cellular phones.
- 18 students owned digital cameras.
- X students owned both cellular phones and digital cameras.
- 2X students owned neither.
To find the total number of students, we can add the number of students who owned cellular phones, the number of students who owned digital cameras, and then subtract the number of students who owned both to avoid counting them twice. Mathematically, the expression can be written as:
Total number of students = (number of students with cell phones) + (number of students with digital cameras) - (number of students with both)
Now, let's plug in the given values:
Total number of students = 23 + 18 - X
To find the value of X, we need additional information or equations. The equation you provided does not directly give a value for X. If you have any additional information or equations, please provide them, and I can help you solve for X.