Initial Commit

2026-03-01 18:50:29 -04:00
parent 261c52d602
commit 364facd9f0
69 changed files with 7829 additions and 87 deletions
--- a/lib/problems/generators/ratio-problems.ts
+++ b/lib/problems/generators/ratio-problems.ts
@@ -0,0 +1,110 @@
+import type { MathProblem, Difficulty } from "../types";
+import { randomInt, randomChoice } from "@/lib/utils";
+import { simplifyRatio, divideInRatio } from "@/lib/math/ratios";
+
+let counter = 0;
+function nextId() {
+  return `rp-${++counter}-${Date.now()}`;
+}
+
+export function generateSimplifyRatio(difficulty: Difficulty): MathProblem {
+  const gcd = randomChoice(difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [3, 4, 5, 6, 7] : [4, 6, 8, 9, 12]);
+  const a = randomInt(1, difficulty === 1 ? 5 : 10) * gcd;
+  const b = randomInt(1, difficulty === 1 ? 5 : 10) * gcd;
+
+  const simplified = simplifyRatio([a, b]);
+
+  return {
+    id: nextId(),
+    prompt: `\\text{Simplify the ratio } ${a}:${b}`,
+    answer: { kind: "ratio", parts: simplified },
+    hints: [
+      `Find the GCD of ${a} and ${b}`,
+      `The GCD is ${gcd}`,
+      `Divide both parts by ${gcd}`,
+    ],
+    steps: [
+      { explanation: `GCD of ${a} and ${b} is ${gcd}` },
+      { explanation: `${a} ÷ ${gcd} = ${simplified[0]}, ${b} ÷ ${gcd} = ${simplified[1]}` },
+      { explanation: `Simplified: ${simplified.join(":")}` },
+    ],
+  };
+}
+
+export function generateDivideInRatio(difficulty: Difficulty): MathProblem {
+  const numParts = difficulty === 3 ? 3 : 2;
+  const parts: number[] = [];
+  for (let i = 0; i < numParts; i++) {
+    parts.push(randomInt(1, difficulty === 1 ? 5 : 9));
+  }
+
+  const sum = parts.reduce((a, b) => a + b, 0);
+  const multiplier = randomChoice(difficulty === 1 ? [2, 3, 4, 5] : [3, 4, 5, 6, 7, 8]);
+  const total = sum * multiplier;
+
+  const values = divideInRatio(total, parts);
+  const intValues = values.map(Math.round);
+
+  const names = ["first share", "second share", "third share"];
+
+  return {
+    id: nextId(),
+    prompt: `\\text{Share } ${total} \\text{ in the ratio } ${parts.join(":")}`,
+    answer: { kind: "ratio", parts: intValues },
+    hints: [
+      `Total parts: ${parts.join(" + ")} = ${sum}`,
+      `One part = ${total} ÷ ${sum} = ${multiplier}`,
+      `Multiply each ratio number by ${multiplier}`,
+    ],
+    steps: [
+      { explanation: `Total parts = ${parts.join(" + ")} = ${sum}` },
+      { explanation: `One part = ${total} ÷ ${sum} = ${multiplier}` },
+      ...parts.map((p, i) => ({
+        explanation: `${names[i]}: ${p} × ${multiplier} = ${intValues[i]}`,
+      })),
+    ],
+  };
+}
+
+export function generateRatioWordProblem(difficulty: Difficulty): MathProblem {
+  const a = randomInt(2, 7);
+  const b = randomInt(2, 7);
+  const diff = Math.abs(a - b);
+
+  if (diff === 0) {
+    return generateDivideInRatio(difficulty);
+  }
+
+  const contexts = [
+    { item: "sweets", nameA: "Josh", nameB: "Nathan" },
+    { item: "marbles", nameA: "Amy", nameB: "Ben" },
+    { item: "stickers", nameA: "Karen", nameB: "Natasha" },
+  ];
+  const ctx = randomChoice(contexts);
+
+  const onePart = randomChoice(difficulty === 1 ? [5, 10, 12] : [6, 8, 9, 15, 20]);
+  const extraAmount = diff * onePart;
+  const totalParts = a + b;
+  const total = totalParts * onePart;
+
+  const bigger = a > b ? ctx.nameA : ctx.nameB;
+  const biggerRatio = Math.max(a, b);
+  const smallerRatio = Math.min(a, b);
+
+  return {
+    id: nextId(),
+    prompt: `\\text{${ctx.item.charAt(0).toUpperCase() + ctx.item.slice(1)} were shared between ${ctx.nameA} and ${ctx.nameB} in the ratio ${a}:${b}. If ${bigger} received ${extraAmount} more ${ctx.item}, find the total shared.}`,
+    answer: { kind: "integer", value: total },
+    hints: [
+      `The difference in ratio parts is ${biggerRatio} - ${smallerRatio} = ${diff}`,
+      `${diff} parts = ${extraAmount}, so 1 part = ${onePart}`,
+      `Total parts = ${a} + ${b} = ${totalParts}`,
+    ],
+    steps: [
+      { explanation: `Difference in parts: ${biggerRatio} - ${smallerRatio} = ${diff}` },
+      { explanation: `${diff} parts = ${extraAmount}, so 1 part = ${extraAmount} ÷ ${diff} = ${onePart}` },
+      { explanation: `Total parts: ${a} + ${b} = ${totalParts}` },
+      { explanation: `Total ${ctx.item}: ${totalParts} × ${onePart} = ${total}` },
+    ],
+  };
+}