Thread: word problem help

120 students were asked about skiing. Here are the results of the poll:
1. Have you skied either cross-country or downhill? Yes: 65 No: 55
2. If you answered Yes to Question 1, did you ski downhill? Yes: 28 No: 37
3. If you answered Yes to Question 1, did you ski country-country? Yes: 45 No: 20
How many students skiied both cross-country and downhill?

I'm not sure why it is 8?

Originally Posted by mjoshua

120 students were asked about skiing. Here are the results of the poll:
1. Have you skied either cross-country or downhill? Yes: 65 No: 55
2. If you answered Yes to Question 1, did you ski downhill? Yes: 28 No: 37
3. If you answered Yes to Question 1, did you ski country-country? Yes: 45 No: 20
How many students skiied both cross-country and downhill?

I'm not sure why it is 8?

Use a Venn-diagram.

I'm still kinda of lost why we use those values in the circles..

I still don't see why

Originally Posted by mjoshua

I still don't see why

Hi mjoshua,

That's the beauty of Venn diagrams. They tell the story visually.

You have a total of 65 people who have skied.

28 of them have skied downhill and 45 of them have skied cross-country.

Whoops! That's a total of 73 people. We only had 65 to start with.

Must be an overlap of 8 people who skied both downhill AND cross-country!

The intersection of the two circles indicates this overlap.

Put an 8 in there and make sure the two whole circles add up to 28 and 45, respectively.

Thanks masters that helped! Just curious though, the "Group Forumla" is kinda the same way right? How would you prove that: Total = Group 1 + Group 2 + Neither - Both is true using a venn diagram/same logic? (These are also common word problems that involve only 2 groups)