[
  "Let Richard have R and Betty have B. R + B = 990. After spending: Betty left with 1/4 B, Richard with 2/3 R. These are equal.",
  "From (1/4)B = (2/3)R, multiply both sides by 12: 3B = 8R, so B = (8/3)R. Substitute: R + (8/3)R = 990 -> (11/3)R = 990 -> R = 270.",
  "Richard spent 1/3 of R = 1/3 x 270 = $90. Answer: Richard spent $90."
]