When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?

Let x represent your age now. Your age 4 years from now will be x+4. Your age 5 years from now will be x+5.
  4(x+4) + 5(x+5) = 10x
  4x + 16 + 5x + 25 = 10x    (eliminate parentheses)
  41 = x    (subtract 9x from both sides, collect terms)
In 3 years, you will be 44 years old.

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Check   4 years from now, you will be 45
  5 years from now, you will be 46.
  4(45) + 5(46) = 180 + 230 = 410, 10 times your current age.

If you wanted to, you could let "a" represent your age 3 years from now. Then you have
  4(a+1) + 5(a+2) = 10(a-3)
  4a + 4 + 5a + 10 = 10a - 30    (eliminate parentheses)
  9a + 14 = 10a - 30    (collect terms)
  14 = a - 30    (subtract 9a)
  44 = a   (add 30 to get age 3 years from now)