Question

The results of a survey of 200 people incoming students show the following results:
75 students own a Playstation
65 students own a Xbox
55 Students own a Nintendo
25 students own at least a PlayStation and an Xbox
20 Students own at least Nintendo and a Playstation
15 students own at least an Xbox and a Nintendo
5 own all three Playstation, Xbox, Nintendo
How many people don't own any video game system?

Answer 1

Can someone help me out?

Answer 2

hey man, lets see what you got today

Answer 3

alright

Answer 4

"How many people don't own any video game system?" is the question.
Is this a algebra question?

Answer 5

This is actually have to do with sets

Answer 6

Do you understand how to set it up

Answer 7

in the first 3 lines, it gives us all the information we need.
P stands for playstation
X stands for x box
N stands for nintendo
? stands for the people that don't have any video game system

200 = 75P + 65X + 55N + ?

25 = P + x
20 = N + X
5 = P + X + N

here is what I could get set up

Answer 8

How do you solve it

Answer 9

have you learned about systems of equations?

Answer 10

yes

Answer 11

great.

...mmm this one is still got me thinking, hold on..

Answer 12

ok

Answer 13

i'm stumped..

Answer 14

Can someone help me solve this

Answer 15

I think I get it now

Answer 16

lets just look at nintendo first.

Answer 17

ok

Answer 18

wait wait sorry, ya i'm no good at this :(
sorry bigtim

Answer 19

I got a number of 65, does that sound right?

Answer 20

not sure

Answer 21

here is what I did, I reversed the order, and started subtacting one group from the next group. we are given number of kids, but what we need to know is how many total systems there are, not how many kids there are.

5 own all three Playstation, Xbox, Nintendo, 5pxn
15 students own at least an Xbox and a Nintendo, 15xn
20 Students own at least Nintendo and a Playstation, 20np
25 students own at least a PlayStation and an Xbox, 25px
55 Students own a Nintendo, 55n
65 students own a Xbox, 65x
75 students own a Playstation, 75p

Answer 22

if 5 kids own all three, then I subtract that from the next three sentances.

5pxn-5= 0pxn
15xn-5 = 10xn
20np-5 = 15np
25px-5 = 20px
55n
65x
75p

Answer 23

so my new set is
0pxn
10xn
15np
20px
55n
65x
75p


now i subtract the new set from the the next set.
0pxn
10xn
15np
20px
55n-10n-15n = 30n
65x-10x-20x=35x
75p-20p-15p=40p

so my new set now is
0pxn
0xn
0np
0px
30n
35x
40p

so there are a total of 30nintendos, 35xboxes and 40 playstations.

Answer 24

30 + 35 + 40 = 135

200-135 = 65
65 students don't have any.