Help with this math question!!!!!!!?

Question

Rena Burkholder records the weather on 30 random days in a year. It rains on 12 days. The sun shines on 17 days. It is neither rainy nor sunny on 6 days.

Using the information above answer the following questions:
a) Draw a venn diagram to represent the situation.
b) How many days is it rainy and sunny??

Please explain how you get the answers. I know the correst answer but I don't know how people get that answer. To make sure, the real answer for number (A) is: rainy=7, sunny=12, both =5.
(B) is: 5

please help!!!!!!!

Answer 1

There were 12 days with rain, 17 with sun, and 6 with neither. Added together, that's 35 days.
But we know there were only 30 days in all, so since 35-30 =5, we know that 5 of the days must be in common ( in other words they were both sunny and rainy - yes it can happen).

So take the 12 rainy days and subtract the 5 days that were in common, getting 7 days of rain only.
Draw a circle with the numbers 7 and 5 in it.

Now take the 17 sunny days and subtract the 5 days in common, getting 12 days of sun only. Write down 12 outside of the first circle (Since the first circle represents rainy days and the 12 days are the days it didn't rain). Now draw a circle around the 12 and the 5. This circle represents the sunny days and the intersection of the two circles represent the days it was both sunny and rainy. But 6 days were neither, so write 6 outside of both circles. Now draw a circle around the entire set of numbers. This circle represents all the days of weather and all the numbers inside (representing all the days) will add up to 30.

It is likely that there are other ways to think about this and solve it. (Just like there are often many ways to solve any problem.) This is the way my mind works and this approach seems to work for me in all situations. Good luck.

Answer 2

Unfortunately, it is hard to draw Venn Diagrams here. If we have 6 non-rain, non-sun days, that leaves 24 days which have either sun, rain, or days with both. Since 12 days have rain and 17 sun, there have to be 12+17-24=5 days with both.