Venn Diagram Car Park Problem: L-plates & GB-plates Explained

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Homework Help Overview

The problem involves a car park scenario with 25 cars, where participants are tasked with determining the distribution of cars with L-plates and GB-plates, including those with neither. The context is centered around Venn diagrams to visualize the relationships between these groups.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants present various attempts at drawing Venn diagrams to represent the distribution of cars with L-plates and GB-plates. They express uncertainty about the numbers assigned to each category and question where their reasoning may be flawed.

Discussion Status

Some participants suggest starting with the cars that have neither plates as a simpler approach. Others have provided specific counts based on their diagrams but are seeking confirmation on their findings. There is ongoing exploration of the correct distribution of cars with L-plates and GB-plates.

Contextual Notes

Participants note that there are 12 cars with neither plates, which impacts the total count of cars with L-plates and GB-plates. The problem constraints include the total number of cars and the specified counts of cars with L-plates and GB-plates.

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Homework Statement


In a car park there are 25 cars, 5 have L-plates, 12 have GB-plates and 12 have neither.
1) How many have an L-plate but not a GB-plate?
2) How many have a GB-plate and an L-plate?

Homework Equations


None here really

The Attempt at a Solution


I got four different drawings each with two venn diagrams.

L-plate =2
Both L and GB-plate = 3
GB-plate = 9

L-plate =1
Both L and GB-plate = 4
GB-plate = 8

L-plate =3
Both L and GB-plate = 2
GB-plate = 10

L-plate =4
Both L and GB-plate = 1
GB-plate = 11

Where am I going wrong?

1) How many have an L-plate but not a GB-plate?
it could be 2, 1, 3 or 4 ?? Not sure which one and why?

2) How many have a GB-plate and an L-plate?
it could be 3, 4, 2 or 1 ?? Not sure which one and why?
 
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Natasha1 said:

Homework Statement


In a car park there are 25 cars, 5 have L-plates, 12 have GB-plates and 12 have neither.
1) How many have an L-plate but not a GB-plate?
2) How many have a GB-plate and an L-plate?

Homework Equations


None here really

The Attempt at a Solution


I got four different drawings each with two venn diagrams.
L-plate =2
Both L and GB-plate = 3
GB-plate = 9
That leaves how many cars without tags?
L-plate =1
Both L and GB-plate = 4
GB-plate = 8
That leaves how many cars without tags?
L-plate =3
Both L and GB-plate = 2
GB-plate = 10
That leaves how many cars without tags?
L-plate =4
Both L and GB-plate = 1
GB-plate = 11
That leaves how many cars without tags?
Where am I going wrong?

1) How many have an L-plate but not a GB-plate?
it could be 2, 1, 3 or 4 ?? Not sure which one and why?

2) How many have a GB-plate and an L-plate?
it could be 3, 4, 2 or 1 ?? Not sure which one and why?
Some of your drawings of Venn diagrams must be incorrect
 
Natasha1 said:

Homework Statement


In a car park there are 25 cars, 5 have L-plates, 12 have GB-plates and 12 have neither.
1) How many have an L-plate but not a GB-plate?
2) How many have a GB-plate and an L-plate?

Start with the 'neithers' -- they're the easiest, no confusion. Place them outside your Venn diagram.
That leaves 13 cars; your three remaining figures should add to 13.
 
Last edited:
I think I've got it... It must be

L-plate =1
Both L and GB-plate = 4
GB-plate = 8
Neither plates (outside both Venn diagrams) = 12
As the total is 13 (total of L-plates, GB-plates or both must = 13)

1) How many have an L-plate but not a GB-plate?
Is 1
2) How many have a GB-plate and an L-plate?
Is 4

Could someone please check and let me know if it's right? Many thanks :)
 
Natasha1 said:
Could someone please check and let me know if it's right? Many thanks :)

Bingo :)
 
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Many thanks :)
 

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