A survey conducted with 30 students revealed that:20 has cell phone 16 has tsblets 4 has neither 2x has both...calculate the value of x
20-2x+2x+16-2x+4=40
40-2x=30
40-30=2x
10÷2x=2x÷2x
5=x
To solve this problem, we can use the principle of inclusion-exclusion.
First, let's break down the information given in the survey:
- There are 30 students in total.
- 20 students have cell phones.
- 16 students have tablets.
- 4 students have neither a cell phone nor a tablet.
- There are 2 students who have both a cell phone and a tablet (represented by 2x).
To calculate the value of x, we need to find the number of students who have both a cell phone and a tablet.
We can start by adding up the number of students who have cell phones and the number of students who have tablets: 20 + 16 = 36.
However, this sum includes the 2x students who have both a cell phone and a tablet. So, we need to subtract the number of students who have both in order to avoid counting them twice.
Let's subtract 2x from the sum of 20 and 16, resulting in: 36 - 2x.
Now, we know that there are 4 students who have neither a cell phone nor a tablet. So, we can subtract this number from the previous result:
36 - 2x = 4.
Simplifying the equation, we have:
36 - 2x = 4.
Now, let's solve for x:
First, subtract 36 from both sides: -2x = 4 - 36 = -32.
Then, divide both sides by -2: x = (-32) / (-2) = 16.
Therefore, the value of x is 16.