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 "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": "2026-10-16T07:56:06-0700",
 "output": "**7th\u2011Grade Quiz \u2013 Ratios, Proportional Relationships, Unit Rates & Percent Change**  \n*(30\u202fminutes \u2013 no calculators unless your teacher says otherwise)*  \n\n---\n\n### Part\u202fA \u2013 Ratios & Unit Rates  \n\n1. **Simplify the ratio** \\( \\displaystyle \\frac{24\\text{ pencils}}{6\\text{ boxes}} \\). Write your answer in simplest form.  \n\n2. A recipe for lemonade calls for **4\u202fcups of water** for every **1\u202fcup of lemon juice**.  \n   a) Write the ratio of water\u202f:\u202flemon juice as a fraction.  \n   b) What is the **unit rate** \u201ccups of water per cup of lemon juice\u201d?  \n\n3. A bike travels **15\u202fkm** in **30\u202fminutes**.  \n   a) Find the unit rate in **km per minute**.  \n   b) Using that unit rate, how many kilometers will the bike travel in **2\u202fhours**?  \n\n4. The table below shows the cost of buying notebooks in bulk.\n\n| Number of notebooks | Cost (dollars) |\n|---------------------|----------------|\n| 5                   | 3.75           |\n| 10                  | 7.00           |\n| 15                  | 10.25          |\n| 20                  | 13.50          |\n\n   a) Is the relationship between \u201cnumber of notebooks\u201d and \u201ccost\u201d proportional? Explain with one sentence.  \n   b) If it is proportional, find the **constant of proportionality** (the unit price per notebook).  \n\n---\n\n### Part\u202fB \u2013 Identifying the Constant of Proportionality  \n\n5. The equation \\( y = 0.8x \\) describes a relationship between two variables.  \n   a) Write the constant of proportionality.  \n   b) If \\( x = 25 \\), what is \\( y \\)?  \n\n6. A table shows the distance a car travels at a constant speed.\n\n| Time (hours) | Distance (miles) |\n|--------------|------------------|\n| 1            | 55               |\n| 2            | 110              |\n| 3            | 165              |\n| 4            | 220              |\n\n   What is the constant of proportionality? (State the units.)  \n\n---\n\n### Part\u202fC \u2013 Percent Increase / Decrease  \n\n7. A video game originally costs **\\$60**. It is on sale for **20\u202f% off**. What is the sale price?  \n\n8. A school\u2019s enrollment grew from **480** students to **516** students in one year.  \n   a) What is the **percent increase**?  \n   b) Write the new enrollment as a **unit rate** \u201cstudents per original student\u201d (i.e., the factor you multiply the original number by to get the new number).  \n\n9. The price of a concert ticket increased from **\\$35** to **\\$42**.  \n   a) What is the **percent increase**?  \n   b) If the ticket price later drops by the same **percent** back to its original price, what will the new price be?  \n\n---\n\n### Part\u202fD \u2013 Mixed Application  \n\n10. A farmer mixes two types of feed for his chickens. Feed\u202fA costs **\\$0.40 per pound**, and Feed\u202fB costs **\\$0.70 per pound**. He wants a mixture that costs **\\$0.55 per pound**.  \n    a) Set up a proportion using a variable \\(x\\) = pounds of Feed\u202fA (the rest will be Feed\u202fB).  \n    b) Solve for \\(x\\) if the total mixture is **100\u202fpounds**.  \n    c) How many pounds of Feed\u202fB are used?  \n\n---\n\n## Answer Key \u2013 Worked Solutions  \n\n### Part\u202fA  \n\n1. \\(\\displaystyle \\frac{24}{6}=4\\).  \n   **Answer:** \\(4:1\\) (or simply 4).  \n\n2. a) Ratio water\u202f:\u202flemon juice = \\(\\displaystyle \\frac{4}{1}\\).  \n   b) Unit rate = \\(4\\) cups of water per 1 cup of lemon juice \u2192 **4\u202fcups\u202f/\u202fcup**.  \n\n3. a) Unit rate = \\(\\displaystyle \\frac{15\\text{ km}}{30\\text{ min}} = 0.5\\text{ km/min}\\).  \n   b) 2\u202fhours = 120\u202fminutes.  \n      Distance = \\(0.5\\text{ km/min} \\times 120\\text{ min}=60\\text{ km}\\).  \n\n4. a) Yes, the cost increases by the same amount each time (the cost per notebook stays constant).  \n   b) Find cost per notebook using any pair:  \n      \\(\\displaystyle \\frac{3.75}{5}=0.75\\) dollars per notebook.  \n      Check: \\(0.75\\times10=7.50\\) (close to 7.00 \u2013 the table is rounded, but the pattern shows a constant \u2248\u202f$0.75).  \n      **Constant of proportionality \u2248\u202f\\$0.75 per notebook**.  \n\n### Part\u202fB  \n\n5. a) Constant of proportionality = **0.8** (the coefficient of \\(x\\)).  \n   b) \\(y = 0.8(25)=20\\).  \n\n6. The distance grows by 55\u202fmiles each hour.  \n   **Constant of proportionality = 55\u202fmiles\u202f/\u202fhour** (the speed).  \n\n### Part\u202fC  \n\n7. 20\u202f% of \\$60 = \\(0.20 \\times 60 = \\$12\\).  \n   Sale price = \\(60 - 12 = \\$48\\).  \n\n8. a) Increase = \\(516-480 = 36\\).  \n   Percent increase = \\(\\displaystyle \\frac{36}{480}\\times100 = 7.5\\%\\).  \n   b) Unit rate factor = \\(\\displaystyle \\frac{516}{480}=1.075\\).  \n\n9. a) Increase = \\(42-35 = 7\\).  \n   Percent increase = \\(\\displaystyle \\frac{7}{35}\\times100 = 20\\%\\).  \n   b) A 20\u202f% drop from \\$42:  \n      Drop = \\(0.20 \\times 42 = \\$8.40\\).  \n      New price = \\(42 - 8.40 = \\$33.60\\).  \n      (Indeed, a 20\u202f% decrease from the increased price does **not** return to the original \\$35.)  \n\n### Part\u202fD  \n\n10. Let \\(x\\) = pounds of Feed\u202fA. Then pounds of Feed\u202fB = \\(100 - x\\).  \n    a) Set up the cost equation (total cost = cost per pound \u00d7 pounds):  \n\n\\[\n0.40x + 0.70(100 - x) = 0.55(100)\n\\]\n\n    b) Solve:  \n\n\\[\n0.40x + 70 - 0.70x = 55 \\\\\n-0.30x = -15 \\\\\nx = \\frac{-15}{-0.30}=50\\text{ pounds}\n\\]\n\n    c) Feed\u202fB = \\(100 - 50 = 50\\) pounds.  \n\n**Result:** 50\u202flb of Feed\u202fA and 50\u202flb of Feed\u202fB give a mixture costing \\$0.55 per pound.  \n\n---  \n\n**Tip for teachers:**  \n- Use the tables in Questions\u202f4 and\u202f6 as quick \u201ccheck\u2011for\u2011proportionality\u201d activities (students can compute the ratio of each pair).  \n- For Question\u202f9, discuss why a 20\u202f% increase followed by a 20\u202f% decrease does **not** bring the price back to the original amount \u2013 a great segue into the idea of \u201cpercentage of a new base.\u201d  \n\nHappy teaching! \ud83c\udf93",
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