Next we work out the “Only Dogs” number of people. Let’s first work out the “Only Cats” value. This is vital information we now use to work on the rest of the problem. Everything Total – No Cats and No Dogs = 28 – 4 = 24. Let’s put down on our diagram all of the information we have been given.įrom the given information we have been able to work out that the circles total is 24. Other people might think that we do not have enough information, and it is therefore impossible to do this problem. This is because some students have both a cat and a dog. Some people, who do not read this question carefully, will simply take the above figures and put them straight into a Venn Diagram like this.Īlways check at the end that the numbers add up to the “E” Grand total.ġ6 + 18 + 4 = 38 which is much bigger than the “E” total of 28.
The 18 total students for Dogs includes people that have both a cat and a dog, as well as people who only have a dog. This means that the total of the Dogs circle is 18. The question states that: “18 students said they had a dog” without the word “only” in there. The above question does not contain the word “only” anywhere in it, and this is an indication that we will have to do some working out. However this time we are given less information, and so we will have work out the missing information. The answer for this question will actually be the same as the Cats and Dogs question in Example 1. We do not need to work out any missing values.Īll we need to do is place the numbers from the word problem onto the standard Venn Diagram and we are done. Our problem is an easy one where we have been given all of the numbers for the items required on the diagram. Image Source: Passy’s World of Mathematics – Copyright 2012 Here is the type of diagram we will need.
Since this question is about dogs and cats, it will require a two circle Venn Diagram. Note that the word “only” is extremely important in Venn Diagram word problems.īecause the word “only” is in our problem text, it makes it an easy word problem. “A class of 28 students were surveyed and asked if they ever had dogs or cats for pets at home.Ĩ students said they had only ever had a dog.Ħ students said they had only ever had a cat.ġ0 students said they had a dog and a cat.Ĥ students said they had never had a dog or a cat.” Let’s start with an easy example of a two circle diagram problem. Know the standard parts of a Venn DiagramĬheck at the end that all the numbers add up coorectly. Read the question carefully and note down all key information.
Venn Diagram Word Problems can be very easy to make mistakes on when you are a beginner.
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