{
  "source_prefix": "Henry Park 2024 P6 Prelim",
  "models": [
    {
      "n": 6,
      "answer": "210",
      "answer_matches_key": true,
      "working": "Yellow is 7 units, brown is 3 units; the difference is \\(7 - 3 = 4\\) units \\(= 84\\), so 1 unit \\(= 21\\). Total \\(= 10\\) units \\(= 10 \\times 21 = 210\\) balls.",
      "spec": {
        "unit_px": 70,
        "bars": [
          {"label": "Brown", "segments": [
            {"u": 1, "fill": "#d9c2a6"}, {"u": 1, "fill": "#d9c2a6"}, {"u": 1, "fill": "#d9c2a6"}]},
          {"label": "Yellow", "segments": [
            {"u": 1, "fill": "#ffe27a"}, {"u": 1, "fill": "#ffe27a"}, {"u": 1, "fill": "#ffe27a"},
            {"u": 1, "fill": "#ffe27a"}, {"u": 1, "fill": "#ffe27a"}, {"u": 1, "fill": "#ffe27a"},
            {"u": 1, "fill": "#ffe27a", "text": "84 more"}]}
        ],
        "total": {"text": "Total = ?", "bars": [0, 1]}
      }
    },
    {
      "n": 13,
      "answer": "390",
      "answer_matches_key": true,
      "working": "Bookshop A: not red \\(= 75\\%\\) of 200 \\(= 150\\). Bookshop B: not red \\(= 40\\%\\) of 600 \\(= 240\\). Total not red \\(= 150 + 240 = 390\\).",
      "spec": {
        "unit_px": 80,
        "bars": [
          {"label": "A (200)", "segments": [
            {"u": 1, "text": "red 50", "fill": "#ffb3b3"},
            {"u": 3, "text": "not red 150", "fill": "#cfe9cf"}]},
          {"label": "B (600)", "segments": [
            {"u": 3, "text": "red 360", "fill": "#ffb3b3"},
            {"u": 2, "text": "not red 240", "fill": "#cfe9cf"}]}
        ]
      }
    },
    {
      "n": 15,
      "answer": "288",
      "answer_matches_key": true,
      "working": "Take the total as 6 units: fiction \\(= 1\\) unit, non-fiction \\(= 5\\) units. Fiction \\(+100\\%\\) adds 1 unit; non-fiction \\(+50\\%\\) adds 2.5 units. Increase \\(= 3.5\\) units \\(= 168\\), so 1 unit \\(= 48\\). Books at first \\(= 6\\) units \\(= 288\\).",
      "spec": {
        "unit_px": 75,
        "bars": [
          {"label": "Fiction", "segments": [
            {"u": 1, "fill": "#dbe9ff"}]},
          {"label": "Non-fiction", "segments": [
            {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"},
            {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}]}
        ],
        "total": {"text": "Total = 6 units = ?", "bars": [0, 1]}
      }
    },
    {
      "n": 19,
      "answer": "1008",
      "answer_matches_key": true,
      "working": "May : June : July \\(= 4 : 5 : 7\\). May \\(= 4\\) units \\(= 336\\), so 1 unit \\(= 84\\). June + July \\(= 5 + 7 = 12\\) units \\(= 12 \\times 84 = 1008\\).",
      "spec": {
        "unit_px": 70,
        "bars": [
          {"label": "May", "segments": [
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"},
            {"u": 1, "fill": "#dbe9ff"}], "brace": {"text": "336"}},
          {"label": "June", "segments": [
            {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"},
            {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}]},
          {"label": "July", "segments": [
            {"u": 1, "fill": "#cfe9cf"}, {"u": 1, "fill": "#cfe9cf"}, {"u": 1, "fill": "#cfe9cf"},
            {"u": 1, "fill": "#cfe9cf"}, {"u": 1, "fill": "#cfe9cf"}, {"u": 1, "fill": "#cfe9cf"},
            {"u": 1, "fill": "#cfe9cf"}]}
        ],
        "total": {"text": "June + July = ?", "bars": [1, 2]}
      }
    },
    {
      "n": 24,
      "answer": "3500 ml",
      "answer_matches_key": true,
      "working": "Total paint used \\(= 5 \\times 420 = 2100\\) ml. The paint left equals 2 containers' worth, so the 2100 ml used equals \\(5 - 2 = 3\\) containers. 3 containers \\(= 2100\\) ml, so 1 container \\(= 700\\) ml. 5 containers at first \\(= 5 \\times 700 = 3500\\) ml.",
      "spec": {
        "unit_px": 90,
        "bars": [
          {"label": "At first (5)", "segments": [
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"},
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}], "brace": {"text": "? ml"}},
          {"label": "Left (2)", "segments": [
            {"u": 1, "fill": "#cfe9cf"}, {"u": 1, "fill": "#cfe9cf"},
            {"u": 3, "text": "used = 2100 ml", "fill": "#ffd0d0"}]}
        ]
      }
    },
    {
      "n": 25,
      "answer": "$63",
      "answer_matches_key": true,
      "working": "Member price per t-shirt \\(= 216 \\div 6 = \\$36\\). This $36 is 75% (after the further 25% off) of the price after the $15 discount, so that price \\(= 36 \\div 0.75 = \\$48\\). Original price \\(= 48 + 15 = \\$63\\).",
      "spec": {
        "unit_px": 80,
        "bars": [
          {"label": "After $15 off", "segments": [
            {"u": 1, "text": "$12", "fill": "#ffe7c2"},
            {"u": 3, "text": "$36 paid (75%)", "fill": "#dbe9ff"}]},
          {"label": "Original", "segments": [
            {"u": 4, "text": "after $15 off = $48", "fill": "#dbe9ff"},
            {"u": 1, "text": "$15", "fill": "#cfe9cf"}], "brace": {"text": "? = $63"}}
        ]
      }
    },
    {
      "n": 29,
      "answer": "30",
      "answer_matches_key": true,
      "working": "Of 500 cookies: chocolate \\(= \\dfrac{3}{5} \\times 500 = 300\\), butter \\(= \\dfrac{1}{4} \\times 500 = 125\\). Raisin \\(= 500 - 300 - 125 = 75\\). Sold \\(= \\dfrac{2}{5} \\times 75 = 30\\) raisin cookies.",
      "spec": {
        "unit_px": 36,
        "bars": [
          {"label": "500 cookies", "segments": [
            {"u": 12, "text": "Chocolate 300", "fill": "#c8a98a"},
            {"u": 5, "text": "Butter 125", "fill": "#ffe7c2"},
            {"u": 3, "text": "Raisin 75", "fill": "#e0b3d6"}]},
          {"label": "Raisin (75)", "segments": [
            {"u": 8, "text": "sold = 30", "fill": "#d49ac4"},
            {"u": 12, "text": "left = 45", "fill": "#f0d9ec"}]}
        ]
      }
    },
    {
      "n": 37,
      "answer": "$112",
      "answer_matches_key": true,
      "working": "Both spend the same amount, so the difference stays \\(210 - 154 = 56\\). After spending, Jason : Ruth \\(= 7 : 3\\); the difference is \\(7 - 3 = 4\\) units \\(= 56\\), so 1 unit \\(= 14\\). Jason kept \\(7\\) units \\(= 98\\). Each spent \\(= 210 - 98 = \\$112\\).",
      "spec": {
        "unit_px": 70,
        "bars": [
          {"label": "Jason left", "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", "text": "= $98"}]},
          {"label": "Ruth left", "segments": [
            {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"},
            {"u": 4, "text": "diff = 56 = 4 units", "fill": "#ffd0d0"}]}
        ]
      }
    },
    {
      "n": 43,
      "answer": "216",
      "answer_matches_key": true,
      "working": "Group Box A's coins in fours: 1 unit is 10-cent and 3 units are 50-cent, worth \\(1(10) + 3(50) = 160\\) cents per group of 4. \\(\\$86.40 = 8640\\) cents, so number of groups \\(= 8640 \\div 160 = 54\\). Coins in Box A \\(= 54 \\times 4 = 216\\); Box B has the same number \\(= 216\\).",
      "spec": {
        "unit_px": 80,
        "bars": [
          {"label": "Box A (4 units)", "segments": [
            {"u": 1, "text": "10c \\u00d7 1", "fill": "#dbe9ff"},
            {"u": 1, "text": "50c", "fill": "#ffe7c2"},
            {"u": 1, "text": "50c", "fill": "#ffe7c2"},
            {"u": 1, "text": "50c", "fill": "#ffe7c2"}], "brace": {"text": "160c per group of 4"}}
        ]
      }
    },
    {
      "n": 48,
      "answer": "4",
      "answer_matches_key": true,
      "working": "Shop Q sold 24 tubs for \\(15(\\$12) + 9(\\$18) = \\$342\\). Shop S sold the same 24 tubs but for \\(342 + 66 = \\$408\\). If all 24 were small \\(= \\$288\\); the extra \\(408 - 288 = \\$120\\) comes from big tubs at \\(\\$6\\) more each, so big \\(= 120 \\div 6 = 20\\) and small \\(= 24 - 20 = 4\\).",
      "spec": {
        "unit_px": 90,
        "bars": [
          {"label": "All 24 small", "segments": [
            {"u": 4, "text": "24 \\u00d7 $12 = $288", "fill": "#dbe9ff"}]},
          {"label": "Shop S actual", "segments": [
            {"u": 4, "text": "$288", "fill": "#dbe9ff"},
            {"u": 1, "text": "extra $120", "fill": "#ffd0d0"}], "brace": {"text": "$408"}}
        ]
      }
    }
  ]
}