math word problem

Question

amy has 27 friends. 19 like hot fudge and 16 like whipped cream and 9 like both. How many do not like hot fudge and whipped cream?

Answer 1

The best way to find this answer is to put Amy's friends in four distinct groups:

1. Friends who only like hot fudge

2. Friends who only like whipped cream

3. Friends who like both hot fudge and whipped cream

4. Friends who do not like either hot fudge or whipped cream.

 

The question already tells us that 9 friends like both, so there are 9 members in group #3.

 

To find the number of friends in groups 1 and 2, all we have to do is subtract the 9 friends that like both hot fudge and whipped cream from each group.

 

19 friends like hot fudge, but 9 of them also like whipped cream.

19 - 9 = 10, so 10 friends only like hot fudge

 

16 friends like whipped cream, but 9 of them also like hot fudge

16 - 9 = 7, so 7 friends only like whipped cream.

 

To recap:

1. 10 friends only like hot fudge

2. 7 friends only like whipped cream

3. 9 friends like both hot fudge and whipped cream

4. Now we need to find out how many friends don't like either hot fudge or whipped cream.

 

Since there are 27 friends in total, and each friend has to fall into one, and only one, of these categories, we can find out how many are in the fourth group by finding the sum of the members in the first three groups and subtracting it from 27.

 

10 + 7 +9 = 26

27 - 26 = 1

 

Therefore, only 1 friend does not like hot fudge or whipped cream.

 

Hope this helps :)