[
  "Let shoes = S. Bag = S + 40. Equation: 2(S+40) + 3S = 460.",
  "Expand: 2S + 80 + 3S = 460. So 5S = 380, S = 76.",
  "Bag = 76 + 40 = 116 dollars. Check: 2x116 + 3x76 = 232 + 228 = 460."
]