[
  "From 1/9 of X = 1/10 of Y, cross-multiply to get the ratio: X/9 = Y/10 -> 10X = 9Y, so X:Y = 9:10.",
  "Let X = 9k and Y = 10k. Since Y - X = 100, then 10k - 9k = k = 100. So X = 900 and Y = 1000.",
  "Sum = X + Y = 900 + 1000 = 1900. Answer: 1900."
]