Math major vs Math+Physics major

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I am currently a B.S math major at a top 50 university. I wanted to know the advantages adding a B.A Physics major would have on my marketability job-wise and admission to a top engineering graduate school once I graduate.
I am thinking of adding the Physics major, but I'm not sure if taking the extra classes would be worth having a math+physics degree. If I add the physics major, I would be able to graduate on time, but it will leave virtually no room for me to take classes for fun. Any advice?
 
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But physics classes are fun! :)

I guess it all depends on what you want to do. If you want to go to grad school for pure math, I imagine it wouldn't help that much. If you want to go to grad school for physics, well then it would probably help quite a bit.
 
If you're going to be an engineer, you'll need to take some physics and some engineering classes. I've heard of physicists getting into engineering in graduate school, but most of the math majors that go for engineering get into highly simulational or theoretical fields (perhaps in electrical or systems/industrial engineering). It'll be a good idea to try and get a minor in engineering or physics, if not a major. Also, since you won't have much time to take that many classes, you'll have to really figure out what exactly you want to do. If it's fluid mechanics then you really don't need to waste time with signal processing, for example.