"use strict";

function round2(x) { return Math.round(x * 100) / 100; }

module.exports = {
  slug: "ratio-and-proportion-solve",
  title: "Solve a proportion a:b = c:x",
  deck_category: "other",
  description: "Solves the missing fourth term of a proportion a:b = c:x.",
  inputs: [
    { name: "a", type: "number", required: true, description: "First term.", min: 0.0000001 },
    { name: "b", type: "number", required: true, description: "Second term." },
    { name: "c", type: "number", required: true, description: "Third term." }
  ],
  outputs: [
    { name: "x", description: "The fourth term that makes a:b = c:x true." }
  ],
  steps: [
    "A proportion a:b = c:x means a/b = c/x.",
    "Cross-multiplying gives a*x = b*c, so x = (b*c) / a.",
    "Round to 2 decimals."
  ],
  constants: [],
  sources: [
    { kind: "edition_page", value: "Standard arithmetic reference (ratio and proportion, cross-multiplication).", title: "Ratio and proportion, cross-multiplication method", publisher: "Standard arithmetic reference", retrieved_utc: "2026-09-30T19:57:00Z", note: "x = b*c/a from a:b = c:x." }
  ],
  disclaimer: null,
  questionText(inputs) {
    return `If ${inputs.a}:${inputs.b} = ${inputs.c}:x, what is x?`;
  },
  run(inputs) {
    const { a, b, c } = inputs || {};
    for (const [name, v] of Object.entries({ a, b, c })) {
      if (typeof v !== "number" || Number.isNaN(v)) throw new Error(`${name} must be a number`);
    }
    if (a === 0) throw new Error("a must be non-zero");
    const x = round2((b * c) / a);
    return { answer: `${x.toFixed(2)}`, values: { x } };
  },
  examples: [
    {
      name: "worked example",
      inputs: { a: 2, b: 3, c: 10 },
      expected: { answer: "15.00" },
      check: "Cross-multiply to check: 2*15=30 and 3*10=30, equal, so x=15.00 is correct."
    },
    {
      name: "test vector: larger numbers",
      inputs: { a: 4, b: 9, c: 16 },
      expected: { answer: "36.00" },
      check: "Cross-multiply to check: 4*36=144 and 9*16=144, equal, so x=36.00 is correct."
    }
  ]
};