How do I draw a ven diagram for this information?

Question

The aliens wanted to try some earth food so this time Stephen takes the 48 of them to an ice cream store. They all order 1 or 2 scoops, in either a waffle or sugar cone.33 order waffle cones.5 order 1 scoop in a sugar cone. 37 order 2 scoops. how many scoops of ice cream are ordered?

Answer 1

It's pretty hard to show a Venn diagram here, but it would look something like this description says:

1. Draw one big circle labeled with a W that denotes the waffle cone selection.

2. Draw another big circle that doesn't cross over the W circle at all, label with an S for sugar cone.

3. Draw another big circle labeled with a 1 that crosses into the S and W circles.

4. Draw another big circle labeled with a 2 that crosses into the S and W circles but not into the 1 circle.

For the above 4 circles, I would suggest making the S and W circles left and right on the page and the 1 and 2 circles above and below.

5. Obviously, if you have 48 aliens and 33 ordered waffle cones, 15 must have ordered sugar cones.

6. 5 ordered 1 scoop in a sugar cone, you would put 5 dots in the area which is intersected by the 1 circle and the S circle.

7. Since 15 ordered sugar cones (from 5 above), 10 must have ordered 2 scoops on a sugar cone, so put 10 dots in the intersection between circle S and circle 2.

8. If 37 total ordered 2 scoops and 10 ordered 2 scoops in a sugar cone, 27 must have ordered 2 scoops in a waffle cone, so put 27 dots in the intersection between circle W and circle 2.

9. If 33 ordered waffles cones and 27 ordered 2 scoops, 6 ordered 1 scoop on a waffle cone, so put 6 scoops in the intersection bewtween circles 1 and W.

How many scoops were ordered? You didn't need a Venn diagram to get that answer, 11 ordered 1 scoop and 37 ordered 2 scoops , so 37*2 + 11 = 74 + 11 = 85 scoops.

Answer 2

Draw a square. Put a vertical line down the middle and a horizontal line across the middle, so that you have four smaller squares.

The left half represents waffle cones. The right half represents sugar cones.

The top half represents 1 scoop. the bottom half represents 2 scoops.

You are told that 5 order 1 scoop in a sugar cone, so the top right square represents those 5 aliens.

You also know that 37 order 2 scoops, so the two bottom squares total 37.

You've account for 42 (5 + 37) aliens by using every square except the top left, so the top left square must be the other 6 aliens (to get to a total of 48). So 6 aliens had 1 scoop in a waffle cone.

You also know that 33 ordered waffle cones, so 27 (33 - 6) must have ordered 2 scoops in a waffle cone. But you don't really need to know that number, or know that 10 ordered 2 scoops in a sugar cone.

Instead what you need to do is calculate the total number of scoops, which equals the number of 1 scoop cones (the top 2 squares) plus twice the number of 2 scoop cones (which you know is 37).

Answer 3

Are you required to solve this using a Venn diagram? Because it is very simple to solve without using one.

If 37 of the aliens ordered two scoops, then since there are 48 aliens, it follows that the other 11 (48 - 37 = 11) ordered only one scoop. So the total number of scoops ordered was 2*37 + 1*11 = 74 + 11 = 85.

Answer 4

I don't know if I can actually draw a diagram in this editor.

Draw a rectangle to represent the entire set. Divide into two parts by a horizontal line. The parts above and below can represent "1Scoop" and "2 Scoop" subsets.

Divide the original rectangle by a vertical line into two. The parts to the left and right can be used to represent "Waffle" and "Sugar"

There will be 4 partitions. The top left will be "W1", top right "S1", bottom left "W2" and bottom right "S2" . (I am using W1 to mean waffle with 1scoop etc.)

Without drawing the diagrams, 37 order 2 scoops, so the remaining 11 order 1 scoop. The total number of scoops = 2x37+11 = 85.