Another venn-diagram question please?

Question

Although the weather was perfect for the beach party, 17 of the 30 people attending got a sunburn and 25 people were bitten by mosquitos. If 12 people, were both bitten and sunburned, how many had neither affliction?

Answer 1

::

sunburn only = 17 - 12 = 5

bitten only = 25 - 12 = 13

total = 30 = 12 + 5 + 13 + neither

neither = 30 - (12 + 5 + 13) = 0

Answer 2

The formula for such a problem is:
Total # People = # sunburned + # bitten - # sunburned and bitten + # neither sunburned or bitten.
So.... Total 30 = 17 sunburned + 25 bitten - 12 neither sunburned or bitten + # neither sunburned or bitten......
therefore 30=17+25-12+x or 30 = 42-12+x or 30=30+x
So X=0 which means everyone was either sunburned or bitten or both. No one escaped!

Answer 3

Let the universal set be equal to 30. In other words this is the amount of people who attended.

so let x be the number of people affected by both afflictions.

so x is 12 based on the info from the question

now 17 is the same as x + 5 or 12 + 5
and 25 is the same as x + 13 or 12 + 13

so all the areas should add up to 30 or the universal set which is 5 + 12 + 13 + number affected by neither, (lets call this number N

so 30 = 5 +12 + 13 + N

30 = 30 + N

N= 0

therefore no one suffered neither afflictions.

Hope this helps

Answer 4

17 sunburnt + 25 bitten= 42 people afflicted
take away the people we double counted from the burnt circle and the bitten circle overlap, so 42-12=30 people bitten or sunburnt. so 30 out of 30 were afflicted.
So number of non afflicted people = 0

Answer 5

4 because the difference between 25 [bitten] and 12[both] is 13 and 17[sunburn]-13=4.

Answer 6

I paused for a sec. but then I actually drew the diagram, ... Zero, None...

Draw it out and you'll see you run out of people before excluding any group.

Answer 7

none