In a survey of 250 households regarding the ownership of desktop and laptop computers, the following information was obtained:
130 households own only desktop computers. 30 households own only laptop computers.
50 households own neither desktop nor laptop computers.
How many households own both desktop and laptop computers?
Please help. thank you
To determine how many households own both desktop and laptop computers, we can start by subtracting the number of households that own only desktop computers and the number of households that own only laptop computers from the total number of households surveyed.
Total households surveyed: 250
Households owning only desktop computers: 130
Households owning only laptop computers: 30
First, let's find the number of households that own either desktop or laptop computers by adding the households owning only desktop computers and the households owning only laptop computers:
130 + 30 = 160
Next, we subtract the number of households owning either desktop or laptop computers from the total number of households surveyed to find the number of households owning neither type:
250 - 160 = 90
Finally, to find the number of households owning both desktop and laptop computers, we can subtract the number of households owning neither type from the total number of households surveyed:
250 - 90 = 160
Therefore, 160 households own both desktop and laptop computers.
To find out how many households own both desktop and laptop computers, we need to use the concept of set theory and Venn diagrams.
Let's start by assuming that the number of households that own both desktop and laptop computers is "x." We know that 130 households own only desktop computers, 30 households own only laptop computers, and 50 households own neither.
Now, let's construct a Venn diagram to represent the information given:
- Start by drawing two overlapping circles, one representing desktop owners and the other representing laptop owners.
- Write "130" inside the circle representing desktop owners (to represent households that own only desktop computers).
- Write "30" inside the circle representing laptop owners (to represent households that own only laptop computers).
- Write "x" inside the overlapping part of the circles (to represent households that own both desktop and laptop computers).
- Finally, write "50" outside the circles (to represent households that own neither desktop nor laptop computers).
Now, we can use the information given to solve for "x." We know that the total number of households surveyed is 250, so we can add up the numbers in the diagram:
130 (only desktop) + x (both) + 30 (only laptop) + 50 (neither) = 250
Simplifying the equation, we get:
x + 210 = 250
By subtracting 210 from both sides of the equation, we find:
x = 250 - 210
Therefore, the number of households that own both desktop and laptop computers is:
x = 40
So, 40 households own both desktop and laptop computers.
people who own both (b) will be counted in both groups (laptop owners and desktop owners)
when you count all of the households, the "both" group is only counted once
130 + 30 + 50 + b = 250