I'm not sure how to solve this: A group of friends went to an amusement park. 10 of them rode the ferris wheel, 15 rode carousel, and 11 rode the roller coaster. 7 of them rode both the ferris wheel & roller coaster. 4 rode both the ferris wheel & carousel. 5 rode both the carousel and roller coaster. 3 rode all three rides. HOw many friends went to the park?

Question

I'm not sure how to solve this: A group of friends went to an amusement park. 10 of them rode the ferris wheel, 15 rode carousel, and 11 rode the roller coaster. 7 of them rode both the ferris wheel & roller coaster. 4 rode both the ferris wheel & carousel. 5 rode both the carousel and roller coaster. 3 rode all three rides. HOw many friends went to the park?

work:
Ferris wheel & roller coaster 7-2 = 5
Ferris wheel & carousel 4-2 = 2
carousel & roller 5-3 = 2
carousel, ferris wheel, & coaster = 3

5 + 2 +2 +3 = 12 people?

Answer 1

These are best done by using Venn diagrams

(google 'Venn diagram' to get a better idea of that)

Here is a nice short youtube video of a problem that resembles yours, and explains it step by step.

http://www.youtube.com/watch?v=MassxXy8iko

draw the 3 circles within the rectangles and follow the steps outlined in the video
you should get 23 going to the park

let me know if you need further help

Answer 2

To solve this problem, we can use a Venn diagram to visualize the information given. Let's create a Venn diagram with three circles representing the three rides - ferris wheel, carousel, and roller coaster.

First, we know that 10 friends rode the ferris wheel, 15 rode the carousel, and 11 rode the roller coaster.

Next, we are given some overlapping information. 7 friends rode both the ferris wheel and the roller coaster, 4 friends rode both the ferris wheel and the carousel, and 5 friends rode both the carousel and the roller coaster. Additionally, we are told that 3 friends rode all three rides.

Let's label the number of friends in each section of the Venn diagram:
- The overlap between ferris wheel and roller coaster: 7 - 3 = 4
- The overlap between ferris wheel and carousel: 4 - 3 = 1
- The overlap between carousel and roller coaster: 5 - 3 = 2

Now, let's add up the number of friends in each section of the Venn diagram:
- Ferris wheel only: 10 - (4 + 1 + 3) = 2
- Carousel only: 15 - (1 + 2 + 3) = 9
- Roller coaster only: 11 - (4 + 2 + 3) = 2

Finally, to find the total number of friends who went to the park, we add up the number of friends in each category:
2 (Ferris wheel only) + 9 (Carousel only) + 2 (Roller coaster only) + 4 (Ferris wheel and roller coaster) + 1 (Ferris wheel and carousel) + 2 (Carousel and roller coaster) + 3 (All three rides) = 23

Therefore, there were 23 friends who went to the amusement park.

These are best done by using Venn diagrams

Thanks!!

To solve this problem, we can use a Venn diagram to visualize the information given. Let's create a Venn diagram with three circles representing the three rides - ferris wheel, carousel, and roller coaster.