In the article below, the author goes through a series of examples, and takes some common answers and explains why they may not be the best answers to use. First of all, if a specific job is named, and the student has not intention going into that field, you just lost him. If the real-world relation you gave to answer the question seems too complicated, you lost him again. The article goes into detail on how NOT to answer the question so that you won't lose your students. It does not, however, give the exact reason you should give to your students. It does give tips on how to approach the question, but in the end, you need to come up with the best answer you can.
The article does go on to say that the student may not ever use the specific topic in everyday life, but the actual processes that go along with that topic are ones that are used in everyday life. For an example, you need to have problem-solving skills to do most mathematical topics, and problem-solving skills are definitely a need for everyday life. I think the author actually does a great job on explaining why some of the common answers aren't good ones as they can make the teacher appear foolish, uninterested, or even giving the student a negative attitude towards mathematics.
In addition to the article, I have also posted a poster that I saw in a mathematics classroom where I was substituting, and I actually think that EVERY mathematics classroom should have this poster. The poster gives a list of many different types of jobs on the top, and along the side it shows what types of mathematics are needed to do that job.
Article: http://blog.mrmeyer.com/wp-content/uploads/Otten_2011MT_reprint.pdf
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