{
 "model": "openai/gpt-oss-20b",
 "provider": "Groq API (free tier)",
 "task": "math7-proportions",
 "prompt": "Create a 10-question quiz for 7th graders on ratios and proportional relationships, including unit rates, percent increase/decrease, and identifying the constant of proportionality from a table and an equation. Include an answer key with worked solutions.",
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 "ran_at": "2026-10-16T08:00:57-0700",
 "output": "**7th\u2011Grade Math Quiz  \nTopic: Ratios & Proportional Relationships**  \n*Time: 30\u202fminutes*  \n*Answer each question in the space provided.*\n\n---\n\n### 1. Unit Rate (Speed)\n\nA cyclist travels **120\u202fkm** in **3\u202fhours**.  \n**a)** What is the cyclist\u2019s speed in km/h?  \n**b)** If the cyclist rides at the same speed, how long will it take to travel 200\u202fkm?\n\n---\n\n### 2. Unit Rate (Cost)\n\nA pack of 8 apples costs **$4.80**.  \n**a)** What is the price per apple?  \n**b)** How many apples can you buy for **$12.00** at that price?\n\n---\n\n### 3. Unit Rate (Fuel Efficiency)\n\nA car travels **300\u202fmiles** on **10\u202fgallons** of gasoline.  \n**a)** What is the car\u2019s fuel efficiency in miles per gallon?  \n**b)** How many gallons are needed to travel 450\u202fmiles at that efficiency?\n\n---\n\n### 4. Percent Increase\n\nA school\u2019s enrollment grew from **1,200** students to **1,320** students.  \nWhat is the percent increase in enrollment?\n\n---\n\n### 5. Percent Decrease\n\nThe price of a textbook dropped from **$45** to **$32**.  \nWhat is the percent decrease in price?\n\n---\n\n### 6. Percent Increase/Decrease (Multiple Choice)\n\nA video game\u2019s price changed from **$60** to **$48**.  \nWhat is the percent change?  \nA) 10\u202f% decrease\u2003B) 20\u202f% decrease\u2003C) 25\u202f% decrease\u2003D) 30\u202f% decrease\n\n---\n\n### 7. Constant of Proportionality \u2013 Table\n\n| Distance (km) | Time (h) |\n|---------------|----------|\n| 30            | 2        |\n| 45            | 3        |\n| 60            | 4        |\n\nAssuming distance and time are directly proportional, what is the constant of proportionality (speed) in km/h?\n\n---\n\n### 8. Constant of Proportionality \u2013 Table\n\n| Weight (kg) | Volume (L) |\n|-------------|------------|\n| 5           | 10         |\n| 10          | 20         |\n| 15          | 30         |\n\nAssuming weight and volume are directly proportional, what is the constant of proportionality (ratio of weight to volume)?\n\n---\n\n### 9. Constant of Proportionality \u2013 Equation\n\nThe relationship between the number of hours studied (**h**) and the score on a test (**S**) is given by  \n\\( S = 5h \\).  \n\nWhat is the constant of proportionality?\n\n---\n\n### 10. Constant of Proportionality \u2013 Equation\n\nThe cost (**C**) in dollars of renting a car for **t** days is described by  \n\\( C = 35t \\).  \n\nWhat is the constant of proportionality?\n\n---\n\n## Answer Key \u2013 Worked Solutions\n\n**1. Unit Rate (Speed)**  \na) Speed = distance \u00f7 time = \\(120 \\text{ km} \u00f7 3 \\text{ h} = 40 \\text{ km/h}\\).  \nb) Time = distance \u00f7 speed = \\(200 \\text{ km} \u00f7 40 \\text{ km/h} = 5 \\text{ h}\\).\n\n**2. Unit Rate (Cost)**  \na) Price per apple = \\( \\$4.80 \u00f7 8 = \\$0.60\\) per apple.  \nb) Apples for $12.00 = \\( \\$12.00 \u00f7 \\$0.60 = 20\\) apples.\n\n**3. Unit Rate (Fuel Efficiency)**  \na) Fuel efficiency = \\(300 \\text{ mi} \u00f7 10 \\text{ gal} = 30 \\text{ mi/gal}\\).  \nb) Gallons needed for 450 mi = \\(450 \u00f7 30 = 15\\) gallons.\n\n**4. Percent Increase**  \nIncrease = \\(1,320 - 1,200 = 120\\).  \nPercent increase = \\(\\frac{120}{1,200} \u00d7 100\\% = 10\\%\\).\n\n**5. Percent Decrease**  \nDecrease = \\(45 - 32 = 13\\).  \nPercent decrease = \\(\\frac{13}{45} \u00d7 100\\% \u2248 28.9\\% \\) (\u2248\u202f29\u202f%).\n\n**6. Percent Change**  \nChange = \\(60 - 48 = 12\\).  \nPercent change = \\(\\frac{12}{60} \u00d7 100\\% = 20\\%\\).  \nAnswer: **B) 20\u202f% decrease**.\n\n**7. Constant of Proportionality \u2013 Table**  \nSpeed = distance \u00f7 time.  \nUsing any row: \\(30 \u00f7 2 = 15\\) km/h.  \nCheck: \\(45 \u00f7 3 = 15\\), \\(60 \u00f7 4 = 15\\).  \nConstant = **15 km/h**.\n\n**8. Constant of Proportionality \u2013 Table**  \nWeight/Volume = \\(5 \u00f7 10 = 0.5\\) kg/L.  \nCheck: \\(10 \u00f7 20 = 0.5\\), \\(15 \u00f7 30 = 0.5\\).  \nConstant = **0.5 kg per liter**.\n\n**9. Constant of Proportionality \u2013 Equation**  \nEquation \\(S = 5h\\) is of the form \\(y = kx\\).  \nThus \\(k = 5\\).  \nConstant = **5** (score points per hour studied).\n\n**10. Constant of Proportionality \u2013 Equation**  \nEquation \\(C = 35t\\) \u2192 \\(k = 35\\).  \nConstant = **35 dollars per day**.\n\n---\n\n**Good luck, and remember to show all your work for full credit!**",
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