10 Paula asked 30 students what they ate for lunch.
All the students had at least a sandwich, salad or fruit.
5 students had a sandwich, salad and fruit.
7 students had a sandwich and fruit.
9 students had a sandwich and salad.
7 students had salad and fruit.
14 students had a sandwich.
7 students had fruit only.
a Draw a Venn diagram to show this information.
looks quite simple,
draw your Venn diagram, label the intersecting circles sw, s and f
place 5 in the intersection of the 3 circles.
Now look at the intersection of th sandwich and fruit, it says 7
but you already placed 5 into part of that region, so that leaves 2 for the part of sw and f but not f
continue in that pattern until all the regions are filled in
Their total should be 30
Students | food
5 | sandwich/salad/fruit
7 | 🍞 sandwich/fruit🍎
9 | 🍞sandwich/salad🍜
7 | 🍜salad/fruit🍊
14 | 🍞sandwich
7 | fruit🍊
49 students are total
Sure! Let's start by drawing three overlapping circles to represent the three food options: sandwich, salad, and fruit.
In the center of the diagram, we will write the number 5, which represents the 5 students who had all three options (sandwich, salad, and fruit).
Next, we will add additional numbers to the overlapping regions to represent the number of students who had combinations of two food options.
In the region where the sandwich and fruit circles overlap, we will write the number 7, which represents the 7 students who had a sandwich and fruit.
In the region where the sandwich and salad circles overlap, we will write the number 9, which represents the 9 students who had a sandwich and salad.
In the region where the salad and fruit circles overlap, we will write the number 7, which represents the 7 students who had salad and fruit.
Next, we will add numbers to the non-overlapping regions to represent the students who had only one food option.
In the sandwich circle, we will write the number 14, which represents the 14 students who had only a sandwich.
In the fruit circle, we will write the number 7, which represents the 7 students who had only fruit.
Finally, in the salad circle, we will write the number x (to be determined later).
The completed Venn diagram representing this information should look like this:
x (salad only)
_________
/ \
/ 5 \
/______/________\
(7) (9)
\______/________\
7
I hope this helps! Let me know if you have any further questions.
To draw a Venn diagram to show this information, you would need three overlapping circles: one for sandwiches, one for salads, and one for fruits.
First, let's label the three circles. Let circle A represent sandwiches, circle B represent salads, and circle C represent fruits.
Next, fill in the numbers given in the question:
- 5 students had a sandwich, salad, and fruit, so this number goes in the overlapping region of all three circles.
- 7 students had a sandwich and fruit, so this number goes in the overlapping region of circles A and C.
- 9 students had a sandwich and salad, so this number goes in the overlapping region of circles A and B.
- 7 students had a salad and fruit, so this number goes in the overlapping region of circles B and C.
- 14 students had a sandwich only, so this number goes in the region of circle A that is not overlapping with the other circles.
- 7 students had fruit only, so this number goes in the region of circle C that is not overlapping with the other circles.
Now, you can draw the Venn diagram with the labeled circles and filled in numbers to visually represent the information provided.