{
  "version": 1,
  "topic": "CE04",
  "title": "Calculate mixing water after rounding cement sacks",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Water for the selected whole-sack batch",
    "premise": "The baseline volume and yield require 235 whole sacks. Only the assumed mixing-water demand per sack varies.",
    "formula": "water = whole sacks × water per sack",
    "variables": "Water in US gallons, sacks as an integer count, recipe input in US gal/sk. Service water is excluded.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Water per sack (US gal/sk) = 6.3",
        "explanation": "The baseline volume and yield require 235 whole sacks. Only the assumed mixing-water demand per sack varies."
      },
      {
        "label": "Select the relation",
        "calculation": "water = whole sacks × water per sack",
        "explanation": "Water in US gallons, sacks as an integer count, recipe input in US gal/sk. Service water is excluded."
      },
      {
        "label": "Substitute the values",
        "calculation": "235 × 6.3 = 1,480.5 US gal",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Mixing water (US gal) = 1480.5; Whole sacks (sk) = 235",
        "explanation": "Water follows the prepared whole-sack batch, not fractional theoretical demand."
      }
    ],
    "result": "Mixing water (US gal) = 1480.5; Whole sacks (sk) = 235",
    "interpretation": "Water follows the prepared whole-sack batch, not fractional theoretical demand.",
    "control": "Water per sack (US gal/sk)",
    "columns": [
      "Water per sack (US gal/sk)",
      "Mixing water (US gal)",
      "Whole sacks (sk)"
    ],
    "rows": [
      [
        5,
        1175,
        235
      ],
      [
        6,
        1410,
        235
      ],
      [
        6.3,
        1480.5,
        235
      ],
      [
        7,
        1645,
        235
      ],
      [
        8,
        1880,
        235
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Water per sack (US gal/sk) = 5. Mixing water (US gal): 1175; Whole sacks (sk): 235.",
      "Water per sack (US gal/sk) = 6. Mixing water (US gal): 1410; Whole sacks (sk): 235.",
      "Water per sack (US gal/sk) = 6.3. Mixing water (US gal): 1480.5; Whole sacks (sk): 235.",
      "Water per sack (US gal/sk) = 7. Mixing water (US gal): 1645; Whole sacks (sk): 235.",
      "Water per sack (US gal/sk) = 8. Mixing water (US gal): 1880; Whole sacks (sk): 235."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Mixing water (US gal) without rounding intermediate values.",
        "answer": "235 × 6.3 = 1,480.5 US gal. Mixing water (US gal) = 1480.5. Water follows the prepared whole-sack batch, not fractional theoretical demand."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Water per sack (US gal/sk) changes from 5 to 8. Other controls remain as stated in the premise. Mixing water (US gal) changes from 1175 to 1880."
      },
      {
        "question": "What would be needed to apply this example to a different physical system?",
        "answer": "Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Water in US gallons, sacks as an integer count, recipe input in US gal/sk. Service water is excluded. Water follows the prepared whole-sack batch, not fractional theoretical demand."
      }
    ]
  },
  "recorded": null
}