{
  "source_prefix": "Maris Stella 2023 P6 Prelim",
  "models": [
    {
      "n": 15,
      "answer": "180",
      "answer_matches_key": true,
      "working": "Men \\(=20\\%=1\\) unit \\(=100\\), so the whole \\(=5\\) units \\(=500\\). Remainder \\(=4\\) units \\(=400\\). Women \\(=55\\%\\) of \\(400=220\\). Children \\(=400-220=180\\).",
      "spec": {
        "unit_px": 70,
        "bars": [
          {"label": "People", "segments": [
              {"u": 1, "text": "men 100", "fill": "#dbe9ff"},
              {"u": 1, "text": "", "fill": "#ffe7c2"},
              {"u": 1, "text": "", "fill": "#ffe7c2"},
              {"u": 1, "text": "", "fill": "#ffe7c2"},
              {"u": 1, "text": "", "fill": "#ffe7c2"}],
           "brace": {"text": "500"}},
          {"label": "Remainder", "segments": [
              {"u": 11, "text": "women 220", "fill": "#cdeccd"},
              {"u": 9, "text": "children ?", "fill": "#f6d6e6"}],
           "brace": {"text": "400"}}
        ]
      }
    },
    {
      "n": 24,
      "answer": "104",
      "answer_matches_key": true,
      "working": "Kingston \\(=8\\) units, Tim \\(=5\\) units. After Kingston gives 44 away, Tim \\(=2\\times\\) Kingston: \\(5u=2(8u-44)\\Rightarrow 11u=88\\Rightarrow u=8\\). Total at first \\(=13u=13\\times 8=104\\).",
      "spec": {
        "unit_px": 60,
        "bars": [
          {"label": "Kingston (before)", "segments": [
              {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"},
              {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"},
              {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}]},
          {"label": "Tim (before)", "segments": [
              {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"},
              {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}]},
          {"label": "Kingston (after)", "segments": [
              {"u": 8, "text": "gave 44 away → 5 units", "fill": "#dbe9ff"}]},
          {"label": "Tim (= 2 × after)", "segments": [
              {"u": 5, "fill": "#ffe7c2"}]}
        ]
      }
    },
    {
      "n": 33,
      "answer": "$3600",
      "answer_matches_key": true,
      "working": "After the brother takes \\(\\dfrac{5}{8}\\) of the remainder, \\(\\dfrac{3}{8}\\) of the remainder is left, which equals \\(\\dfrac14\\) of the salary. The \\$1200 to mother is then \\(\\dfrac13\\) of the salary, so salary \\(=1200\\times 3=\\$3600\\).",
      "spec": {
        "unit_px": 90,
        "bars": [
          {"label": "Salary", "segments": [
              {"u": 1, "text": "mother $1200", "fill": "#dbe9ff"},
              {"u": 1, "text": "remainder $2400", "fill": "#ffe7c2"},
              {"u": 1, "text": "", "fill": "#ffe7c2"}],
           "brace": {"text": "salary = $3600"}},
          {"label": "Remainder", "segments": [
              {"u": 1, "text": "brother", "fill": "#cdeccd"},
              {"u": 1, "fill": "#cdeccd"},
              {"u": 1, "fill": "#cdeccd"},
              {"u": 1, "fill": "#cdeccd"},
              {"u": 1, "fill": "#cdeccd"},
              {"u": 1, "text": "left = ¼ salary", "fill": "#f6d6e6"},
              {"u": 1, "fill": "#f6d6e6"},
              {"u": 1, "fill": "#f6d6e6"}],
           "brace": {"text": "$2400"}}
        ]
      }
    },
    {
      "n": 42,
      "answer": "1120",
      "answer_matches_key": true,
      "working": "Work backwards. After the 3 siblings: \\(100+3\\times 40=220\\). Before Troy: \\((220+30)\\times 2=500\\). Before Samuel: \\((500+60)\\times 2=1120\\). Peter had 1120 at first.",
      "spec": {
        "unit_px": 90,
        "bars": [
          {"label": "At first", "segments": [
              {"u": 1, "text": "half + 60 → Samuel", "fill": "#dbe9ff"},
              {"u": 1, "text": "other half = 500", "fill": "#ffe7c2"}],
           "brace": {"text": "1120"}},
          {"label": "After Samuel", "segments": [
              {"u": 1, "text": "half + 30 → Troy", "fill": "#cdeccd"},
              {"u": 1, "text": "left 220", "fill": "#f6d6e6"}],
           "brace": {"text": "500"}},
          {"label": "Left 220", "segments": [
              {"u": 1, "text": "40 × 3 siblings = 120", "fill": "#dbe9ff"},
              {"u": 1, "text": "100 left", "fill": "#ffe7c2"}]}
        ]
      }
    },
    {
      "n": 43,
      "answer": "160",
      "answer_matches_key": true,
      "working": "Men \\(+\\) women \\(=400\\). Remaining \\(=\\dfrac23 m+\\dfrac25 w=224\\). Times \\(\\dfrac32\\): \\(m+\\dfrac35 w=336\\). Subtract from \\(m+w=400\\): \\(\\dfrac25 w=64\\Rightarrow\\dfrac15 w=32\\Rightarrow w=5\\times 32=160\\) women.",
      "spec": {
        "unit_px": 70,
        "bars": [
          {"label": "Men", "segments": [
              {"u": 2, "text": "⅓ left", "fill": "#dbe9ff"},
              {"u": 1, "text": "left venue", "fill": "#eaeaea"}]},
          {"label": "Women", "segments": [
              {"u": 1, "fill": "#ffe7c2"},
              {"u": 1, "fill": "#ffe7c2"},
              {"u": 1, "text": "⅕ × w each", "fill": "#ffe7c2"},
              {"u": 1, "fill": "#eaeaea"},
              {"u": 1, "fill": "#eaeaea"}],
           "brace": {"text": "w = 160"}}
        ],
        "total": {"text": "400 adults", "bars": [0, 1]}
      }
    },
    {
      "n": 45,
      "answer": "80",
      "answer_matches_key": true,
      "working": "Chocolate : strawberry \\(=3:5\\). The difference \\(=2\\) units \\(=28\\), so \\(1\\) unit \\(=14\\). Strawberry \\(=5\\) units \\(=70\\). Vanilla \\(=\\) strawberry \\(+10=70+10=80\\).",
      "spec": {
        "unit_px": 80,
        "bars": [
          {"label": "Chocolate", "segments": [
              {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}]},
          {"label": "Strawberry", "segments": [
              {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"},
              {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "text": "diff = 2 units = 28", "fill": "#ffe7c2"}]},
          {"label": "Vanilla", "segments": [
              {"u": 1, "fill": "#cdeccd"}, {"u": 1, "fill": "#cdeccd"}, {"u": 1, "fill": "#cdeccd"},
              {"u": 1, "fill": "#cdeccd"}, {"u": 1, "fill": "#cdeccd"},
              {"u": 1, "text": "+10", "fill": "#f6d6e6"}],
           "brace": {"text": "? = 80"}}
        ]
      }
    }
  ]
}