{
  "source_prefix": "Nan Chiau 2022 P6 Prelim",
  "models": [
    {
      "n": 10,
      "answer": "64 min",
      "answer_matches_key": true,
      "working": "Total time \\(= 72 \\times 4 = 288\\) min. Anna \\(= 288 - (80 + 74 + 70) = 288 - 224 = 64\\) min.",
      "spec": {
        "unit_px": 70,
        "bars": [
          {"label": "Anna", "segments": [{"u": 2, "text": "?", "fill": "#dbe9ff"}]},
          {"label": "Belinda", "segments": [{"u": 2, "text": "80", "fill": "#ffe7c2"}]},
          {"label": "Colin", "segments": [{"u": 2, "text": "74", "fill": "#ffe7c2"}]},
          {"label": "Danny", "segments": [{"u": 2, "text": "70", "fill": "#ffe7c2"}]}
        ],
        "total": {"text": "288 (= 72 x 4)", "bars": [0, 1, 2, 3]}
      }
    },
    {
      "n": 11,
      "answer": "$14",
      "answer_matches_key": true,
      "working": "Left with \\(\\dfrac{4}{5}\\), so spent \\(= 1 - \\dfrac{4}{5} = \\dfrac{1}{5}\\) of \\(\\$350 = \\$70\\) over 5 days. Per day \\(= \\$70 \\div 5 = \\$14\\).",
      "spec": {
        "unit_px": 90,
        "bars": [
          {"label": "Mary", "segments": [
            {"u": 1, "text": "spent", "fill": "#ffd6d6"},
            {"u": 1, "text": "left", "fill": "#dbe9ff"},
            {"u": 1, "text": "left", "fill": "#dbe9ff"},
            {"u": 1, "text": "left", "fill": "#dbe9ff"},
            {"u": 1, "text": "left", "fill": "#dbe9ff"}
          ], "brace": {"text": "$350"}}
        ]
      }
    },
    {
      "n": 14,
      "answer": "28%",
      "answer_matches_key": true,
      "working": "\\(\\$45\\) is 90% of the usual price, so 10% \\(= \\$5\\) and usual price \\(= \\$50\\). Final price \\(= \\$45 - \\$9 = \\$36\\). Total discount \\(= \\$50 - \\$36 = \\$14 = \\dfrac{14}{50} \\times 100\\% = 28\\%\\).",
      "spec": {
        "unit_px": 60,
        "bars": [
          {"label": "Usual price", "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"}, {"u": 1, "fill": "#dbe9ff"},
            {"u": 1, "text": "10%", "fill": "#ffd6d6"}
          ], "brace": {"text": "$50 (100%)"}},
          {"label": "After 10% off", "segments": [{"u": 9, "text": "$45 (90%)", "fill": "#dbe9ff"}]}
        ]
      }
    },
    {
      "n": 22,
      "answer": "\\(\\dfrac{1}{10}\\)",
      "answer_matches_key": true,
      "working": "Not blue \\(= 1 - \\dfrac{7}{10} = \\dfrac{3}{10}\\). Pink : white \\(= 2 : 1\\), so white \\(= \\dfrac{1}{3}\\) of \\(\\dfrac{3}{10} = \\dfrac{1}{10}\\).",
      "spec": {
        "unit_px": 60,
        "bars": [
          {"label": "All beads", "segments": [
            {"u": 7, "text": "blue (7/10)", "fill": "#dbe9ff"},
            {"u": 2, "text": "pink", "fill": "#ffd6f0"},
            {"u": 1, "text": "white", "fill": "#eeeeee"}
          ], "brace": {"text": "1 whole (10 units)"}}
        ]
      }
    },
    {
      "n": 23,
      "answer": "$2000",
      "answer_matches_key": true,
      "working": "Shop B selling price \\(= \\$1500 \\times \\dfrac{80}{100} = \\$1200\\). Shop A sells at the same \\(\\$1200\\) after 40% off, so \\(\\$1200\\) is 60% of A's usual price: \\(\\$1200 \\div 60 \\times 100 = \\$2000\\).",
      "spec": {
        "unit_px": 60,
        "bars": [
          {"label": "Shop A usual", "segments": [
            {"u": 6, "text": "$1200 (60%)", "fill": "#dbe9ff"},
            {"u": 4, "text": "40% off", "fill": "#ffd6d6"}
          ], "brace": {"text": "? (100%)"}},
          {"label": "Shop B usual", "segments": [
            {"u": 8, "text": "$1200 (80%)", "fill": "#ffe7c2"},
            {"u": 2, "text": "20% off", "fill": "#ffd6d6"}
          ], "brace": {"text": "$1500 (100%)"}}
        ]
      }
    },
    {
      "n": 32,
      "answer": "434",
      "answer_matches_key": true,
      "working": "Red : Blue \\(= 2 : 11\\). Difference \\(= 11 - 2 = 9\\) units \\(= 1953\\), so 1 unit \\(= 1953 \\div 9 = 217\\). Red \\(= 2\\) units \\(= 2 \\times 217 = 434\\).",
      "spec": {
        "unit_px": 60,
        "bars": [
          {"label": "Red", "segments": [
            {"u": 1, "fill": "#ffd6d6"}, {"u": 1, "fill": "#ffd6d6"}
          ], "brace": {"text": "?"}},
          {"label": "Blue", "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"}, {"u": 1, "fill": "#dbe9ff"},
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}
          ]}
        ],
        "total": {"text": "9 units = 1953 more", "bars": [0, 1]}
      }
    },
    {
      "n": 36,
      "answer": "86 pencils",
      "answer_matches_key": true,
      "working": "9 notebooks + 54 pencils \\(= \\$64.80 =\\) 24 notebooks, so 54 pencils \\(=\\) 15 notebooks. 1 notebook \\(= \\$64.80 \\div 24 = \\$2.70\\); 15 notebooks \\(= \\$40.50 =\\) 54 pencils, so 1 pencil \\(= \\$0.75\\). Pencils for \\(\\$64.80 = 64.80 \\div 0.75 = 86.4 \\to\\) at most 86.",
      "spec": {
        "unit_px": 70,
        "bars": [
          {"label": "9 NB + 54 P", "segments": [
            {"u": 3, "text": "9 notebooks", "fill": "#dbe9ff"},
            {"u": 5, "text": "54 pencils", "fill": "#ffe7c2"}
          ], "brace": {"text": "$64.80"}},
          {"label": "24 notebooks", "segments": [
            {"u": 8, "text": "24 notebooks", "fill": "#dbe9ff"}
          ], "brace": {"text": "$64.80"}}
        ]
      }
    },
    {
      "n": 41,
      "answer": "$27",
      "answer_matches_key": true,
      "working": "A : (B+C) \\(= 3 : 5 \\to\\) scale to total 40: A \\(= 15\\), B+C \\(= 25\\). C : (A+B) \\(= 2 : 3 \\to\\) scale to total 40: C \\(= 16\\), A+B \\(= 24\\). So A \\(= 15\\), C \\(= 16\\), B \\(= 40 - 15 - 16 = 9\\). C \\(-\\) B \\(= 16 - 9 = 7\\) units \\(= \\$21\\), so 1 unit \\(= \\$3\\). Beth paid the least \\(= 9\\) units \\(= \\$27\\).",
      "spec": {
        "unit_px": 75,
        "bars": [
          {"label": "Anne", "segments": [{"u": 3, "text": "15 units", "fill": "#dbe9ff"}]},
          {"label": "Beth", "segments": [{"u": 2, "text": "9 units (?)", "fill": "#d6f0d6"}]},
          {"label": "Crystal", "segments": [{"u": 3, "text": "16 units", "fill": "#ffe7c2"}]}
        ],
        "total": {"text": "C - B = 7 units = $21", "bars": [1, 2]}
      }
    },
    {
      "n": 42,
      "answer": "180",
      "answer_matches_key": true,
      "working": "Pineapple sold \\(= 100\\% - 75\\% = 25\\%\\) of all sold \\(= 350\\), so sold \\(= 1400\\) and total \\(= 1400 \\div \\dfrac{7}{10} = 2000\\). Unsold \\(= \\dfrac{3}{10}\\) of \\(2000 = 600\\). Pineapple unsold \\(= 30\\%\\) of \\(600 = 180\\).",
      "spec": {
        "unit_px": 60,
        "bars": [
          {"label": "Sold (7/10)", "segments": [
            {"u": 5, "text": "nutella 75% (1050)", "fill": "#ffe7c2"},
            {"u": 2, "text": "pineapple 25% (350)", "fill": "#ffd6c2"}
          ], "brace": {"text": "1400"}},
          {"label": "Unsold (3/10)", "segments": [
            {"u": 1, "text": "pineapple 30% (180)", "fill": "#ffd6c2"},
            {"u": 2, "text": "nutella 70% (420)", "fill": "#ffe7c2"}
          ], "brace": {"text": "600"}}
        ],
        "total": {"text": "Total = 2000", "bars": [0, 1]}
      }
    },
    {
      "n": 45,
      "answer": "12 cookies",
      "answer_matches_key": true,
      "working": "Small boxes hold \\(\\dfrac{7}{9}\\), large boxes hold \\(\\dfrac{2}{9}\\) of the cookies, so small total : large total \\(= 7 : 2\\). Let each small box \\(= s\\), each large box \\(= s + 4\\). Then \\(14s : 3(s+4) = 7 : 2\\), so \\(2 \\times 14s = 7 \\times 3(s+4)\\): \\(28s = 21s + 84\\), \\(7s = 84\\), \\(s = 12\\). Each small box held 12 cookies.",
      "spec": {
        "unit_px": 75,
        "bars": [
          {"label": "Small boxes", "segments": [
            {"u": 7, "text": "14 small boxes (7/9)", "fill": "#dbe9ff"}
          ]},
          {"label": "Large boxes", "segments": [
            {"u": 2, "text": "3 large boxes (2/9)", "fill": "#ffe7c2"}
          ]}
        ],
        "total": {"text": "All cookies (9 units)", "bars": [0, 1]}
      }
    }
  ]
}