7
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If

  • 2010THADFA + 2014IFTH = WHAT IF?,
  • 1996RE + 2012NE = SANTA FE,
  • 1987INTHWO + 2002HA = IT TAKES TWO,
  • 1975THWI + 1994BEANTHBE = HOME,

then (in increasing order of difficulty)

  • 2007XA + 2009NETONO = ?,
  • 1966CA + ? = ? (two solutions)
  • 2015HA + ? + ? = ?

Super extra bonus:

  • 2015AL + ? + ? + ? = ?
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4
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The first one is:

I'M ALIVE

The second is

2014IFTH, giving WHAT WOULD YOU DO?
1970GE, giving SO WHAT?

The third is

1970LOLAKIGE and 2015SORO, giving RIGHT HAND MAN

Super extra bonus

2012GHTHMU, 1983BA, and 1972PI, giving WITH YOU

And here's the key:

The equations are in the form of [four-digit year of Broadway* debut][first two letters of each of the words in the title] + same = SONG TITLE COMMON TO BOTH MUSICALS

e.g.,

2010 THE ADDAMS FAMILY + 2014 IF/THEN = WHAT IF?
1996 RENT + 2012 NEWSIES = SANTA FE
1987 INTO THE WOODS + 2002 HAIRSPRAY = IT TAKES TWO
1975 THE WIZ + 1994 BEAUTY AND THE BEAST = HOME

2007 XANADU + 2009 NEXT TO NORMAL = I'M ALIVE
1966 CABARET + 2014 IF/THEN = WHAT WOULD YOU DO?
1966 CABARET + 1970 GEORGY = SO WHAT?
2015 HAMILTON + 1970 LOVELY LADIES, KIND GENTLEMEN + 2015 SOMETHING ROTTEN = RIGHT HAND MAN

2015 ALLEGIANCE + 2012 GHOST THE MUSICAL + 1983 BABY + 1972 PIPPIN = WITH YOU

* Ho ho! "Broad"-mindedness!

As hinted to in the comments:

Adding the word "THE" to a song from Cabaret gives us 1991 MISS SAIGON (THE TELEPHONE SONG)

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  • $\begingroup$ Your first one is correct as well as one of your second ones. Keep it up! $\endgroup$ – Will Jan 7 '16 at 22:20
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    $\begingroup$ Two different "addends" yield two different "sums." $\endgroup$ – Will Jan 7 '16 at 22:24
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    $\begingroup$ You won't need to change/add any words, though you can find a third solution by adding "THE" to the beginning of one to match the other. $\endgroup$ – Will Jan 7 '16 at 22:30
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    $\begingroup$ @Will then we'd be talking about 1991MISA $\endgroup$ – question_asker Jan 7 '16 at 22:34
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    $\begingroup$ @AZGreenTea I fleshed it out a bit in the bottom chunk of spoilertext, take a look $\endgroup$ – question_asker Jan 8 '16 at 13:17

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